Question

f(x)=5/x^2+sinx
How do you find f '(x)?

Answer 1

is it
\[f(x)=\frac{5}{x^2}+\sin(x)\] or
\[f(x)=\frac{5}{x^2+\sin(x)}\]?

Answer 2

The first one

Answer 3

ok then take the derivative piece by piece
you know the derivative of sine?

Answer 4

cos

Answer 5

ok good
how about the derivative of \(\frac{5}{x^2}\)?

Answer 6

-10x/x4

Answer 7

if you want you can write is as
\[5x^{-2}\] and use the power rule

Answer 8

-10x^-3

Answer 9

or you can do what you did, but then make sure to cancel an \(x\) top and bottom, because
\[-\frac{10x}{x^4}=-\frac{10}{x^3}\]

Answer 10

same answer either way, and now you are done
answer :
\[-\frac{10}{x^3}+\cos(x)\]

Answer 11

Thanks

Answer 12

yw