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To start off with, we have the expression y = x^x and we want to differentiate it. A clever way to do this would be to first remember implicit differentiation and start by taking the natural logarithm of ...

The question is pretty straightforward and asks you to find the derivative of y, which is a function of x. The most simple way to do this is to first eliminate the brackets and then derive. Thus we get y=...

Part a:f(x) = 4x^1.5 + 48x^-0.5 - 8^0.5Finding the gradient function, f'(x) = 6x^0.5 - 24x^-1.5At the stationary point, the gradient is zero, so f'(x) = 0...

The turning point of a curve is the point at which it will turn, therefore, either the maximum or minimum point. Firstly, you need to expand out the brackets so the equation looks like a standard curve eq...

One good way is to use the formula y - y₁ = m(x - x₁)where (x₁,y₁) is a point on the line and m is the gradient of the line. This is derived from the definitio...