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First we want to state what Newton's first law is. 

Newton's first law of motion states that an object at rest will remain at rest, or if in motion, will remain in motion at a constant ve...

When you see a fraction as the power like this you want to try to simplify it to things that you can do (like power of 1/2 or 2). 125 is one of the key numbers to remember when preparing for your GCSEs...

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...