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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 ...

We can set arctan(x) = y. Remember that arctan(x) is the inverse of tan(x), so we can take the tangent of both sides to give: tan(arctan(x)) = x = tan(y). Tan(x) has the standard derivative of sec^2(x) (w...

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...