Question

f(x)=sin^(7)x

The 7 is an exponent and the x is not.

Find the derivative.

Answer 1

Let u=sin(x)
f(x)=u⁷
f'(x)=d (u⁷) /dx
= d (u⁷) /du . du/dx
= 7u⁶ . d(sin(x))/dx
= 7 sin⁶(x) cos(x)

Answer 2

let z = sin x
then f(z) = z^7
and dz/dx = cos x
df(z)/ dz = 7 z^6
d f(x) dx = d f(z)/dz * dz/dx
= 7 z^6 cos x = 7 sin^6 x cos x

Answer 3

I got the same answer but for some reason, it's not the right answer(webwork). Thanks though!

Answer 4

I got the same answer as Damon and MathMate and I'll give 1000:1 odds that we are right.

(It could be that they have a variation of our answer. An easy way to check if two different looking answers are both correct, pick any obscure angle, e.g. 78º, and sub it into both answers. If you get the same result .....)

Answer 5

If it's web exercise, try the equivalent forms:

7sin⁵(x) sin(2x) /2
or
3.5sin⁵(x) sin(2x)