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To differentiate this kind of expression you would need to use implicit differentiation. 

Although it may sound new, you already have all the skills you need to be able to do it. We will ...

First of all note the dx means that we are integrating with respect to x.

So lets integrate each term seperately..

3x^2 ---> (raise the power by one then divide by the ne...

Fristly, we should integrate the whole equation,

y=∫ 6-8x+x^4 dx

y=6x-4x^2+x^5/5+C

Then, subsitituting values to find the C,

4=61-41^2+1...

As we have to differentiate both x and y, we must use implict differentiation for the y by differentiating it with respect to x (also written as d/dx)

5x² -> 10x (multiply t...

I think it’s best I work through an example with you as these problems can vary quite a lot, but the general methods used are the same.
Example: Use the substitution u=x²+5 to find: The in...