Question

If f(x) = sin^2(3-x), f'(0)=

Answer 1

do you take derivative first or plug in 0?

Answer 2

do you go to depaul

Answer 3

Always always always take the derivative first, otherwise you are taking the derivative a constant, which would just be zero.

Answer 4

yes we are looking for f'(0)
so we need to find f'
to do that we need to differentiate f

Answer 5

\[f'(x)=-2\sin(3-x)\cos(3-x)\] replace x by zero

Answer 6

minus sign in front because you need the derivative of
\[3-x\] as the last step in the chain rule

Answer 7

f and f' are two different functions
f'(0) tells you that you want to plug 0 into f' not f

Answer 8

so my answer is negative...right?