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This is a question taken from a core 4 paper and is a typical example of a differential equation question.

The first thing to notice about this equation is that it is "separable"...

Find dy/dx where y = (x²+7)^1/2
=> 1/2(x²+7)^-1/2 * d/dx(x²+7)  By the chain rule
=> 1/2(x²+7)^-1/2 * 2x
=>...

To work out the gradient of a function f(x), we need to differentiate it with respect to x, to give us f'(x). If x = a at a point, then the gradient of f(x) at that point is f'(a) (substitute a in plac...

Let us denote sin(nx) = u(x), where u is a function of x. The equation is now therefore f(x) =(u(x))^n.

For simplicity, we will write that as f(x) = u^n

By the chain rule, w...

First simplify the expression; 3x^(2)-3 to get;

[(x+1)/3(x^(2)-1)] - [1/(3x+1)] 

Using the fact that x^(2)-1 is the difference of two squares, we can simplify it to;