1. ## derivative question

im doing question

f(x) = (x^2 - [e^(2x)] + [sin^3 (x)])^7, find f'(x)

so far,
f'(x)= 7(x^2 - [e^(2x)] + [sin^3 (x)])^6 * (x^2 - [e^(2x)] + [sin^3 (x)])'
= 7(x^2 - [e^(2x)] + [sin^3 (x)])^6 *@@@@@@@@@@@@@@

for @@@@@@@@...
i know i have to derivate (x^2 - [e^(2x)] + [sin^3 (x)])'
i was wondering if i just derivate like 2x - 2e^2x + 3(sinx)^2 (cosx) ?

if so, do i have to derivate "x" from"
(sinx)^3
3(sinx)^2 (cosx) <--- from here, do i have to derivate "x"? like 3(sinx)^2 (cosx)(x)' ?

2. Originally Posted by haebinpark
im doing question

f(x) = (x^2 - [e^(2x)] + [sin^3 (x)])^7, find f'(x)

so far,
f'(x)= 7(x^2 - [e^(2x)] + [sin^3 (x)])^6 * (x^2 - [e^(2x)] + [sin^3 (x)])'
= 7(x^2 - [e^(2x)] + [sin^3 (x)])^6 *@@@@@@@@@@@@@@

for @@@@@@@@...
i know i have to derivate (x^2 - [e^(2x)] + [sin^3 (x)])'
i was wondering if i just derivate like 2x - 2e^2x + 3(sinx)^2 (cosx) ?

if so, do i have to derivate "x" from"
(sinx)^3
3(sinx)^2 (cosx) <--- from here, do i have to derivate "x"? like 3(sinx)^2 (cosx)(x)' ?
I explained to you about the derivative of the 'x' in the other thread. You understand it, right?

$f(x) = (x^2 - e^{2x} + sin^3x)^7$
$f'(x) = 7(x^2 - e^{2x} + sin^3x)^6 \times (2x - e^{2x} \times 2 + 3sin^2x \times cosx)$

I've pointed out the places where I've multiplied something because of the chain rule with $\times$. Do you see how that works. If you need anymore help, feel free to ask.

Hope I helped you