1. TrashMan914

If you say so.

2. Dodo1

Thank you!

3. TrashMan914

You're welcome.

4. Dodo1

$w=\frac{ \sqrt(x) }{ 2^2+t3^t }$

5. Dodo1

sorry it should be sart (t)

6. Dodo1

and find dw/dt

7. mathsmind

that is simple

8. mathsmind

do u want the answer or do u want a step by step solution?

9. mathsmind

when u answer my question i sill proceed

10. TrashMan914

Math, you can't simply give them the answer. It's against CoC. Guide them to it, so they can answer it themselves.

11. Dodo1

step by step pleae!

12. Dodo1

13. .Sam.

Quotient rule with respect to (t)..

14. Dodo1

g(x)f(x)'-f(x)g(x)'/g(x)^2

15. .Sam.

This right$w=\frac{\sqrt{x}}{3^t t+2^2}$

16. .Sam.

You can use chain rule as well

17. Dodo1

therefore, (2t62+t3^t)d/dx(sqrt(t)-sqrt(t)(2t^2+t3^t)/(2t^2+t3^t)^2

18. .Sam.

Followed by product rule

19. Dodo1

I dont how how to caculate the root.

20. Dodo1

and how to do (2t62+3t^3) to derivative?

21. .Sam.

The root "x" is just acted like constant, ignore it

22. Dodo1

my teacher told me to do something like 1/2x^-1/2? is it wrong

23. .Sam.

is the question this?$\Large w=\frac{\sqrt{x}}{3^t t+2^2}$

24. Dodo1

no $w=\frac{ Sqrt(t) }{ 2t^2+t3^t }$

25. .Sam.

You sure? the answer is $\Large \frac{dw}{dt}=-\frac{3^t+t \left(3^t (9 \log )+6\right)}{2 t^{3/2} \left(2 t+3^t\right)^2}$

26. Dodo1

no you dont use log. i have not learnt that yet

27. .Sam.

$\Large \frac{dw}{dt}=-\frac{3^t+t \left(3^t ( \ln(9) )+6\right)}{2 t^{3/2} \left(2 t+3^t\right)^2}$ This?

28. Dodo1

mm maybe but is it possible to go simpler than this?

29. Dodo1

is it not possible?

30. .Sam.

no its not possible, other results are

31. Dodo1

I only have learned power rule, exponential rule and product rule. ( chain rule)

32. mathsmind

step one use the quotient rule..

33. mathsmind

the only trick u have here is 3^t, u may use the table or D-operator...

34. Dodo1

yes I did! its above. I dont know how to break down and power rules.

35. Dodo1

please show me step by step.

36. mathsmind

let me show u how to solve 3^t

37. mathsmind

is that the part ur are struggling with right

38. mathsmind

i will show u step by step but let's break this down

39. Dodo1

Yes :( t3^t

40. Dodo1

thank you so much. I want to cry right now

41. mathsmind

stop crying and fight for the answer

42. Dodo1

ok, i wil! thanks

43. mathsmind

trust me i will let u solve this problem

44. Dodo1

you wont help me?

45. Dodo1

so far i have got

46. mathsmind

damn i wrote the answer on another post hehehe

47. mathsmind

$\[u = 3^t, \space du = 3^t \ln(3)$\]

48. Dodo1

$\frac{ (2t^2+t3^t)(\sqrt(x)'-\sqrt(x)(2t^2+t3^t) }{ (2t^2+t3^t)^2 }$

49. mathsmind

$u = 3^t, \space du = 3^t \ln(3)$

50. mathsmind

now do u know how this happend

51. Dodo1

but its t3^t?

52. mathsmind

forget the t for now because i want to show u bit by bit

53. mathsmind

because with the t we will get into the product rule

54. Dodo1

ok, I got it. i am taking note hold on

55. Dodo1

du_3^t why its In(3)?

56. mathsmind

good question, now u r starting to listen and that is a good sign of learning...

57. mathsmind

u= 3^t what happens if you take the natural log of both sides?

58. Dodo1

mm im not sure, , negative numbers?

59. mathsmind

ln(u) = ln(3^t)

60. mathsmind

now do u know how to differentiate both sides?

61. Dodo1

No I am not sure.

62. Dodo1

mutiply?

63. mathsmind

ok no problem, first of all we need some log rules

64. mathsmind

ln(u) = tln(3)

65. mathsmind

did u see what happend to t?

66. Dodo1

power of t went outside of 3 and In?

67. mathsmind

yes this is a primitive ln rule

68. Dodo1

Oh I see.

69. Dodo1

Do i use this everytime i do product?

70. mathsmind

now if y=ln(x) what is y'?

71. mathsmind

u mean every time u have a log of a power?

72. Dodo1

ok, I got it.

73. mathsmind

sorry power of a log

74. mathsmind

now if y=ln(x) what is y'?

75. Dodo1

power of a log, ok !

76. Dodo1

mmm.. y=In/(x)?

77. mathsmind

no y=ln(x) ->y'=1/x

78. Dodo1

wow, thats new to me!

79. mathsmind

this is basic differentiation of natural log

80. mathsmind

so now back to our question ln(u) = tln(3) differentiate both sides...

81. Dodo1

tIn(3)/x

82. mathsmind

ok let me make this even simple

83. mathsmind

so u don't get confused

84. Dodo1

85. mathsmind

$\frac{d}{dt}a^t=a^tln(a)$

86. mathsmind

can u memorize this for now and take it for granted

87. Dodo1

Ok,

88. mathsmind

ok use this formula and tell me what is 3^t?

89. mathsmind

hint: a=3

90. Dodo1

mmm.... 3^tIn(3)?

91. mathsmind

well done so memorize that please take a note and keep it in ur mind the same way u know ur name...

92. Dodo1

Ok I will.

93. Dodo1

whats the next step?

94. mathsmind

sorry i was replying to another post on set theory ok

95. Dodo1

its okay.

96. mathsmind

now tell me how would u differentiate? $2^2+t3^t$

97. Dodo1

you mean 2t^2?

98. Dodo1

2^tIn(2)+3tIn(3)?

99. mathsmind

no 2^2 is a constant

100. mathsmind

look at it again

101. mathsmind

trust me by solving this part we are more than half way of solving the problem

102. mathsmind

$2^2+t3^t$

103. mathsmind

2^2=4 so when u differentiate a constant u get zero right!?

104. Dodo1

Oh! so its (4t)?

105. mathsmind

ok listen let me solve it

106. mathsmind

can u see how this happened?

107. mathsmind

using the product rule

108. Dodo1

No, wheres 2 go? theres no 2 in the answer

109. mathsmind

$u=2^2+t3^t \rightarrow du=(3^t+t3^tln3))dt$

110. mathsmind

listen y=4, what is y'?

111. Dodo1

y=-4?

112. Dodo1

zero? beacuse its constant

113. mathsmind

zero well done, so y=2^2, y'=?

114. Dodo1

zero?

115. mathsmind

yes well done

116. mathsmind

so differentiate now t3^t

117. Dodo1

3^3In(t)?

118. Dodo1

no its 3 ^tIn(3)?

119. mathsmind

$u=2^2+t3^t \rightarrow du=(3^t+t3^tln3))dt$

120. mathsmind

do u know the product rule?

121. Dodo1

I am not sure

122. mathsmind

uv'+u'v???

123. mathsmind

do u know that rule?

124. Dodo1

yes I do qutiotinent rule?

125. mathsmind

no i said product rule..

126. mathsmind

do u want me to solve the whole thing then u may go and think about it?

127. Dodo1

sorry no.

128. Dodo1

129. Dodo1

the whole thing and if i have a question can i ask?

130. mathsmind

then how come u are solving such a problem when u need the fundamentals?

131. Dodo1

I have rules here but im confused how i am apply to . I am able to solve the basic problems

132. Dodo1

i have test next week and I want to do good :(

133. Dodo1

134. mathsmind

I am and i will i promised

135. Dodo1

Thank you so much.

136. mathsmind

can u memorize the followings for me ...!

137. mathsmind

if u have u x v then when u want to differentiate it we use something called the product rule...

138. Dodo1

Ok thank you for the fact.

139. mathsmind

example :

140. mathsmind

if u= x^2 and v = e^x, and we were asked to find the derivative of(uv)

141. mathsmind

we apply this rule u v' + u' v

142. Dodo1

ok!

143. mathsmind

so what u do is u=x^2, u'=2x, v=e^x, u=e^x

144. mathsmind

now can u put the above in the following u v' + u' v

145. Dodo1

mm for my question?

146. mathsmind

no for my question

147. mathsmind

if u= x^2 and v = e^x, and we were asked to find the derivative of(uv) so what u do is u=x^2, u'=2x, v=e^x, u=e^x u v' + u' v

148. Dodo1

ok, x^2(e^x)+2x(ve^x)

149. mathsmind

well done but without the v

150. Dodo1

without v in the end?

151. mathsmind

look at what u wrote

152. Dodo1

yes,

153. mathsmind

what is the v doing in the equation and u got rid of it by subbing the functions in terms of x

154. Dodo1

Oh! sorry yes.

155. mathsmind

ok good now solve for ur question t3^t

156. Dodo1

how?

157. mathsmind

using the product rule then one u just solved above

158. mathsmind

so use the same steps i showed u

159. Dodo1

$f(x)(2t^2+t3^t)(sqrtx)-(sqrtx)(2t^2+t3^t)$ from the producet rule?

160. mathsmind

no i said solve this one t2^t, please follow what i am asking u to do...not ur own rules or derrieres

161. Dodo1

but thats what i have told in the class something like that. or maybe I was wrong. could you show me everything and the answer?

162. Dodo1

right now, I am very confused. ;/ sorry

163. mathsmind

yes but don't forget we decided to break it a part then when we join everything together u'll see the final answer

164. Dodo1

O. I see sorry i was misleading

165. mathsmind

ok then lead now, so wat is diff of t3^t?

166. Dodo1

(t)(3^t)"+t?

167. mathsmind

use the u v' + u' v rule that i just showed u

168. Dodo1

(t)(3^t)+(3^t)(t)?

169. mathsmind

i just told u how to find u' of 3^t

170. mathsmind

i told u to memorize or take a not of it

171. mathsmind

\Large w=\frac{\sqrt{t}}{3^t t+2^2}

172. mathsmind

$\Large w=\frac{\sqrt{t}}{3^t t+2^2}$

173. mathsmind

this is ur equation right?

174. Dodo1

no.

175. Dodo1

its 2t^2+t3^t

176. mathsmind

oh ok

177. mathsmind

$\Large w=\frac{\sqrt{t}}{3^t t+2t^2}$

178. mathsmind

ok let's us apply the quotient rule

179. mathsmind

so let u =t^(1/2) and v=2t^2+t3^t, so what would u', and v' be?

180. mathsmind

or what would du=? and dv=?

181. Dodo1

uv'=vu"

182. Dodo1

(t^1/2)(2t^2+t3^t)+(2t^2+t3^t)

183. mathsmind

u = t^(1/2) that mean u'=(1/2)t^(-(1/2))

184. Dodo1

yes, i got it

185. Dodo1

ops sorry

186. mathsmind

good girl now tell me

187. mathsmind

if v=2t^2+t3^t what is v'?

188. Dodo1

how did you guess that i was a girl. 3^2in(3)?

189. mathsmind

why do u think i am wrong?

190. Dodo1

?

191. mathsmind

$v=2t^2+t3^t \rightarrow v'=4t+3^t+t(3^tln(3))$

192. mathsmind

are u there or surprise?

193. Dodo1

sorry i was looking above to recall again.

194. mathsmind

i told u to write

195. mathsmind

write on a piece of paper

196. Dodo1

I am.

197. mathsmind

$\frac{g(x)f(x)'-f(x)g(x)'}{g(x)^2}$

198. Dodo1

yes,

199. mathsmind

$g(x)=\sqrt{t} \space and \space f(x)=2t^2+t3^t$

200. Dodo1

plug into the equation right?

201. mathsmind

yes

202. Dodo1

but f'(x) and g"(x) needs to be calculated differently

203. mathsmind

yes

204. mathsmind

g(x) =t^(1/2), what is g'(x)?

205. Dodo1

1/2t^-(1/2)

206. mathsmind

how?

207. mathsmind

nope try again

208. mathsmind

recall $nt^{(n-1)}$

209. mathsmind

hint n=(1/2)

210. mathsmind

r u there?

211. Dodo1

(1/2) t^-(1/2)

212. mathsmind

well done

213. mathsmind

if u solve this one the ur almost done with the question

214. mathsmind

$f(t)=2t^2+t3^t \space f'(t)?$

215. mathsmind

are u there?

216. Dodo1

t3^t(in3)?

217. mathsmind

what happened to the 2t^2 and the product rule, if u look up i solved this for like 23084920384 times

218. Dodo1

4t+2^t+t3^t(In3)

219. mathsmind

good now plug the whole thing in the quotient rule

220. Dodo1

Oh I see thank you! i got it~

221. Dodo1

:)

222. mathsmind

ya but that is not the end

223. mathsmind

u still have more to the problem

224. Dodo1

sorry could you wait for 5 mins? im going back to my room and change to my comp?