Question

Find the Derivative
3x^4 + cot2x

Answer 1

Remember the power rule and the chain rule. And also the fact that you can break up a derivative that is the sum of things... which has a name that I don't remember. :D (Sum rule, maybe?)

Answer 2

Can you help me solve for it?

Answer 3

I did help you. What part are you having trouble with?

Answer 4

Not exactly, I'm not sure how to break it down?

Answer 5

You can find the derivative of \(3x^4\) and \(\cot 2x\) separately and then add them together.

So we'll start with \(3x^4\). Do you remember the power rule?

Answer 6

yea, it will be 12x^3.

Answer 7

Ok, so it will be \(12x^3 + \frac{d}{dx}(\cot 2x)\).
Do you know the derivative of the cotangent?

Answer 8

yea its -csc^2x

Answer 9

Yes. So now just apply the chain rule and you have the answer.

Answer 10

so will the answer be
\[f'(x)= 12x^3 \cot2x+ 3x^4(-\csc^2x)\]