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godorovg
 2 years ago
3x^3+2x^2 +X+5 the derivative
evalauate y' when x=3 need a little help bit rusty
godorovg
 2 years ago
3x^3+2x^2 +X+5 the derivative evalauate y' when x=3 need a little help bit rusty

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godorovg
 2 years ago
Best ResponseYou've already chosen the best response.1in order to the first you lower the power by one like this 3x^2+2x^1+5 that is der right?

UnkleRhaukus
 2 years ago
Best ResponseYou've already chosen the best response.1you also have to divide by the original index

godorovg
 2 years ago
Best ResponseYou've already chosen the best response.1you divide by 3 because of 3x^3

godorovg
 2 years ago
Best ResponseYou've already chosen the best response.1so if I divide by 3, than that would make this x^2 instead of 3x^2 I am on the right track?

UnkleRhaukus
 2 years ago
Best ResponseYou've already chosen the best response.1opps ive got mixed up

UnkleRhaukus
 2 years ago
Best ResponseYou've already chosen the best response.1i should have said times by the index \[y(x)=ax^n\qquad\Rightarrow\qquad y'(x)=anx^{n1}\]

UnkleRhaukus
 2 years ago
Best ResponseYou've already chosen the best response.1so sorry if i confused you

godorovg
 2 years ago
Best ResponseYou've already chosen the best response.1so times by index makes 3x^3 Y' 6x^2 right?

UnkleRhaukus
 2 years ago
Best ResponseYou've already chosen the best response.1not quite \[y(x)=3x^3\qquad y'(x)=3\times3x^2\]

godorovg
 2 years ago
Best ResponseYou've already chosen the best response.1here is what I know y' when doing this you lower the power by one and something??

UnkleRhaukus
 2 years ago
Best ResponseYou've already chosen the best response.1when taking the derivative multiply by the power and then lower the power

godorovg
 2 years ago
Best ResponseYou've already chosen the best response.1so you are telling that power before lowering divide to y'

godorovg
 2 years ago
Best ResponseYou've already chosen the best response.1like this 4x^3 so that would be 'y 4 right?

UnkleRhaukus
 2 years ago
Best ResponseYou've already chosen the best response.1i ment times when i said divide originally , dont divide when taking the derivative

godorovg
 2 years ago
Best ResponseYou've already chosen the best response.1can we start over plz..

UnkleRhaukus
 2 years ago
Best ResponseYou've already chosen the best response.1\[y(x)=ax^n\qquad\Rightarrow\qquad y'(x)=n\times ax^{n1}\] \[y(x)=4x^2\qquad\Rightarrow\qquad y'(x)=2\times 4x^{21}\]

godorovg
 2 years ago
Best ResponseYou've already chosen the best response.1okay so the power is what you are times before lowering the power?

godorovg
 2 years ago
Best ResponseYou've already chosen the best response.1so for another example 10X^5 y'(x) 50x^4

UnkleRhaukus
 2 years ago
Best ResponseYou've already chosen the best response.1you got it \(\checkmark\)

godorovg
 2 years ago
Best ResponseYou've already chosen the best response.1so back to the problem now

UnkleRhaukus
 2 years ago
Best ResponseYou've already chosen the best response.1\[y(x)=3x^3+2x^2 +x+5\]\[y'(x)=\]

UnkleRhaukus
 2 years ago
Best ResponseYou've already chosen the best response.1not quite, note that \[x=x^1\]\[5=5x^0\]

UnkleRhaukus
 2 years ago
Best ResponseYou've already chosen the best response.1ok lets do this one term at a time \[(3x^3)^\prime=\]

UnkleRhaukus
 2 years ago
Best ResponseYou've already chosen the best response.1right, now \[(2x^2)^\prime=\]

UnkleRhaukus
 2 years ago
Best ResponseYou've already chosen the best response.1you have the first two terms right,

UnkleRhaukus
 2 years ago
Best ResponseYou've already chosen the best response.1\[f(x)=x=x^1\] \[f^\prime(x)=1\times x^{11}=x^0=1\]

UnkleRhaukus
 2 years ago
Best ResponseYou've already chosen the best response.1the derivative of the last term \[g(x)=5=5x^0\] \[g^\prime(x)=0\times 5x^{01}=\]

UnkleRhaukus
 2 years ago
Best ResponseYou've already chosen the best response.1yeah the derivative of a constant is always zero

godorovg
 2 years ago
Best ResponseYou've already chosen the best response.1so the end number unless it has a power drop off?

UnkleRhaukus
 2 years ago
Best ResponseYou've already chosen the best response.1\[f(x)=x^2+5\qquad f'(x)=2x\]\[g(x)=x^2+9\qquad g'(x)=2x\]\[h(x)=x^2−71\qquad f'(x)=2x\]

UnkleRhaukus
 2 years ago
Best ResponseYou've already chosen the best response.1that last one is ment to be h'

godorovg
 2 years ago
Best ResponseYou've already chosen the best response.1cool love it so far because in math you can't drop anything, in calc 1 you can this is way cool..

godorovg
 2 years ago
Best ResponseYou've already chosen the best response.1do you have time to do one more?

UnkleRhaukus
 2 years ago
Best ResponseYou've already chosen the best response.1yeah can you get the answer to you original question now?

UnkleRhaukus
 2 years ago
Best ResponseYou've already chosen the best response.1\[y(x)=3x^3+2x^2 +x+5\] \[y~'(x)=\]

UnkleRhaukus
 2 years ago
Best ResponseYou've already chosen the best response.1\[\Large\color\red\checkmark\]

godorovg
 2 years ago
Best ResponseYou've already chosen the best response.1okay any other tips here?

UnkleRhaukus
 2 years ago
Best ResponseYou've already chosen the best response.1\[y'(x)=\frac{\text dy(x)}{\text dx}\]

UnkleRhaukus
 2 years ago
Best ResponseYou've already chosen the best response.1its just a different notation, they men the same thing

UnkleRhaukus
 2 years ago
Best ResponseYou've already chosen the best response.1the second has a bit more information because it explicitly say that we are to take the derivative of the function with respect to x, ie we look at the power of the x terms,

godorovg
 2 years ago
Best ResponseYou've already chosen the best response.1so the power on the is 1 right?

godorovg
 2 years ago
Best ResponseYou've already chosen the best response.1just to let know, I am in college not high school

UnkleRhaukus
 2 years ago
Best ResponseYou've already chosen the best response.1\[y(x)=x=x^1\] \[\frac{\text dy(x)}{\text dx}=y'(x)=1\times x^{11}=x^0=1\]

UnkleRhaukus
 2 years ago
Best ResponseYou've already chosen the best response.1im not sure what you mean by this dx(x)^1?dx

UnkleRhaukus
 2 years ago
Best ResponseYou've already chosen the best response.1dx(x)^1/dx \[=\large \frac{\text d(x)^1}{\text dx}\]?

godorovg
 2 years ago
Best ResponseYou've already chosen the best response.1yes that is what I meant to type

UnkleRhaukus
 2 years ago
Best ResponseYou've already chosen the best response.1\[\frac{\text d(x)}{\text dx}=\frac{\text d(x^1)}{\text dx}=1\times x^0=1\]

UnkleRhaukus
 2 years ago
Best ResponseYou've already chosen the best response.1im not sure if i am answer your question?

godorovg
 2 years ago
Best ResponseYou've already chosen the best response.1okay now for the last question here how do this with y"(x) sin

UnkleRhaukus
 2 years ago
Best ResponseYou've already chosen the best response.1should we evaluate y' in the first question when x=3 before that?

godorovg
 2 years ago
Best ResponseYou've already chosen the best response.1y'(x) 9x^2+4x+1 so plug in 3 so we have y'(x) 9x^2 (3) +4x(3) +1 which is y'(x) 27x^2+ 12X +1

UnkleRhaukus
 2 years ago
Best ResponseYou've already chosen the best response.1\[y(x)=3x^3+2x^2+x+5\] \[y'(x)=9x^2+4x+1\] \[y'(3)=9(3)^2+4(3)+1=9\times3\times3+4\times3+1\]

UnkleRhaukus
 2 years ago
Best ResponseYou've already chosen the best response.1when you evaluate a function at a particular x value you substitute this value for x in the equation, there should be no x in left when evaluated

godorovg
 2 years ago
Best ResponseYou've already chosen the best response.1sorry i mess me up by not putting the like this (3)^2

godorovg
 2 years ago
Best ResponseYou've already chosen the best response.1so the answer is F'(3) 81x^2 + 12X +1
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