Question

Find the derivative of the function y=x^2 sin^4 x + x cos^-2 x.

Answer 1

Are you fmailiar with product rule and chain rule?

Answer 2

We went over it in class recently, so i'm still new to it.

Answer 3

Well, first of all, notice that you have two functions there.
Product rule is: \(\sf \color{red}{\frac{d}{dx}~f(x) [g(x)]=f(x) \frac{d}{dx}g(x)+g(x)\frac{d}{dx}f(x)}\)

f(x) = x\(^2\), while g(x) = sin\(^4\)(x)

Answer 4

Does that make sense?

Answer 5

yeah

Answer 6

NO NO NO SORRY! Derivative of OUTSIDE multiplied by INSIDE!
So, for sine, you have \(\sf \color{purple}{[sin(x)]^4}\), Yes? It is the same thing as sin\(^4\)(x). Your

so your outside is the power! You know derivative of a power? Yes.
then multiply it by the INSIDE, which is sin(x).

Answer 7

I think I got it from here, it was just a little hazy. Thanks!

Answer 8

For instance, yours would be \(\sf \color{blue}{\frac{d}{dx}[sin(x)]^4}\) = \(\sf \color{green}{4[sin(x)]^3 \times \frac{d}{dx}sin(x)}\)