Rohangrr
Use the limit definition to compute the derivative, f'(x),
\[f(x)=\frac { 1 }{ 2 } x\frac { 3 }{ 5 } \]



This Question is Closed

mathslover
Best Response
You've already chosen the best response.
0
oh k progression or in progress?
MAN AT WORK :P

chemENGINEER
Best Response
You've already chosen the best response.
0
Answer on Progress

waterineyes
Best Response
You've already chosen the best response.
0
Oh wow what a question...!!

mathslover
Best Response
You've already chosen the best response.
0
rohangrr is typing a reply...

mathslover
Best Response
You've already chosen the best response.
0
oh k here we go

Rohangrr
Best Response
You've already chosen the best response.
4
Use the limit definition to compute the derivative, f'(x), \[f(x)=\frac { 1 }{ 2 } x\frac { 3 }{ 5 } \]

Mimi_x3
Best Response
You've already chosen the best response.
1
derivative from the first principle..?

waterineyes
Best Response
You've already chosen the best response.
0
I am not typing..

mathslover
Best Response
You've already chosen the best response.
0
dw:1345962336537:dw

Mimi_x3
Best Response
You've already chosen the best response.
1
\[\frac{dy}{dx} = \lim_{x \rightarrow 0} \frac{f(x+h)f(x)}{h} \]

Mimi_x3
Best Response
You've already chosen the best response.
1
mathslover; its from the first principle..

mathslover
Best Response
You've already chosen the best response.
0
oh sorry

Rohangrr
Best Response
You've already chosen the best response.
4
\[\huge f'\quad (x)\quad =\lim _{ x\rightarrow 0 } \frac { f(x+\triangle x)f(x) }{ \triangle x } \]
\[\huge \quad =\lim _{ x\rightarrow 0 } \frac { \frac { 1 }{ 2 } (x+\triangle x)\frac { 3 }{ 5 } \{ \frac { 1 }{ 2 } x\frac { 3 }{ 5 } \} }{ \triangle x } \]
What will be after this

hartnn
Best Response
You've already chosen the best response.
3
first of all the limit would be h>0 !!
then u cancel,x/2 and 3/5 in numerator.....

hartnn
Best Response
You've already chosen the best response.
3
i mean delta x >0

Rohangrr
Best Response
You've already chosen the best response.
4
Okay then

hartnn
Best Response
You've already chosen the best response.
3
then u will simply get:dw:1345962738189:dw

mathslover
Best Response
You've already chosen the best response.
0
the same I got but my method was wrong :(

Rohangrr
Best Response
You've already chosen the best response.
4
\quad =\lim _{ \triangle x\rightarrow 0 } \frac { \frac { 1 }{ 2 } x+\frac { 1 }{ 2 } \triangle x\frac { 3 }{ 5 } \frac { 1 }{ 2 } x+\frac { 3 }{ 5 } \} }{ \triangle x }

Rohangrr
Best Response
You've already chosen the best response.
4
is this the final answer

Rohangrr
Best Response
You've already chosen the best response.
4
dw:1345963107126:dw

Rohangrr
Best Response
You've already chosen the best response.
4
Srously IM confused

hartnn
Best Response
You've already chosen the best response.
3
dw:1345963124504:dw

Rohangrr
Best Response
You've already chosen the best response.
4
dw:1345963183321:dw

Rohangrr
Best Response
You've already chosen the best response.
4
dw:1345963244684:dw

myininaya
Best Response
You've already chosen the best response.
0
Do you still have a question?

Rohangrr
Best Response
You've already chosen the best response.
4
Hi @myininaya I didnt observe u here

myininaya
Best Response
You've already chosen the best response.
0
Yes. I'm here.

Rohangrr
Best Response
You've already chosen the best response.
4
Thanks guys

Callisto
Best Response
You've already chosen the best response.
3
First principle:
\[f'(x) =\lim_{Δ x \rightarrow 0}\frac{f(x+Δ x)f(x)}{Δ x}\]
When \(f(x) = \frac{1}{2}x  \frac{3}{5}\),
\[f'(x) =\lim_{Δ x \rightarrow 0}\frac{[\frac{1}{2}(x+Δ x)\frac{3}{5}](\frac{1}{2}x  \frac{3}{5})}{Δ x}\] \[=\lim_{Δ x \rightarrow 0}\frac{\frac{1}{2}x+\frac{1}{2}Δ x\frac{3}{5}\frac{1}{2}x + \frac{3}{5}}{Δ x}\] \[=\lim_{Δ x \rightarrow 0}\frac{\frac{1}{2}Δ x}{Δ x}\] \[=\lim_{Δ x \rightarrow 0}\frac{\frac{1}{2}\cancel{Δ x}}{\cancel{Δ x}}\] \[=\lim_{Δ x \rightarrow 0}\frac{1}{2}\] \[=...\]
Wow! I'm tooooo late!

Rohangrr
Best Response
You've already chosen the best response.
4
But u r still alive

waterineyes
Best Response
You've already chosen the best response.
0
But I am still in confusion now..

waterineyes
Best Response
You've already chosen the best response.
0
To Whom should I give the medal ??

hartnn
Best Response
You've already chosen the best response.
3
what confusion u have?

waterineyes
Best Response
You've already chosen the best response.
0
No, it is now clear...

hartnn
Best Response
You've already chosen the best response.
3
ok..