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Find dy/dx where y = (x 2 +7) 1/2 => 1/2(x 2 +7) -1/2 * d/dx(x 2 +7) By the chain rule => 1/2(x 2 +7) -1/2 * 2x => x(x 2 +7) -1/2 Remember that x 1/2 = sqrt(x) and x -1 = 1/x => x/sqrt(x 2 +7)

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 place of x...

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, we know that f'(x) = df/dx = (df/du...

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; [(x+1)/3(x+1)(x-1)] - [1/(3x+1)] which sim...

This is a standard parametric equations question, it is important that the methodology behind answering this question is understood. For part a) we simply use the chain rule (dy/dx = dy/dt X dt/dx) and the r...