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A derivative is the result of an operation called differentiation. If we differentiate something, a function, the result tells us how much the function changes with respect to a chosen variable. For insta...

The important thing to note is that examiners always give the minimum amount of information for the question to still be answerable. If you have not used all the information then you probably haven't answ...

We will be using the quotient rule, although the product rule is also usable and can be run through if the student wishes. Firstly, define u = 8x, v = x-8 for simplicity. Then clearly u' = 8, v' = 1, and ...

For this we must use the chain rule. We start by defining x³ as a new variable, u = x³ Can then rewrite the expression as y = sin(u) Chain rule tells us that dy/dx = (dy/du)(du/dx) W...

As both equations are equal to y, we can combine them to create a single equation in terms of x: x^3 - x^2 -5X + 7 = x + 7. Shift the equation so the left hand side is equal to 0 on the right: x^3 - x^2 -...