how to find the derivative of the integral

Question

It asks me to find the derivative of d/dx ∫0 to x² ln(7+t²)dt

So in my notes I have ln(7+t^2) underlined as the derivative  so I just thought I would plug in x^2 and I got

ln(7+x^4) as my answer but it marked me wrong. I don't understand because I followed then steps my teacher gave me so I was jest wondering what I did wrong.

 

the other question I had like this was to find the derivative of ∫t to pi  cos(z³)dz  but I have no guess as to how to do this since I only have examples in my notes and book of ones that go from 0 to a variable...

Could you please explain what I should do?

Answer 1

You need to include one extra factor, namely the derivative of the upper limit, i.e. 2x, because that upper limit is other than just plain x.  This is a chain rule consideration.

 

BTW, you employed the word "it" rather often; this is an example of an indefinite antecedent.  Instead, you should have said something like "My homework problem..." or "the online system marked it wrong."