Question

Let f(x)=8(sin(x))^x. Find f′(3).
f′(3)=

Answer 1

First you have to find out what f'(x) is, and then plug 3 into that.

Answer 2

d/dx [8(sin(x))^x] = 8 x [(sin(x))^(x-1)] cos(x)
if x = 3 then
8*3 [ sin^2 (3)] cos(3) ]
I assume x is in radians

Answer 3

If u and v are functions of x, then d/dx u^v is a combination of the power rule and the exponent rule:
d/dx u^v = v u^(v-1) u' + lnu u^v v'
So, d/dx (sinx)^x = x (sinx)^(x-1) * cosx + ln sinx * (sinx)^x * 1

Answer 4

Missed that, use oobleck solution !