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If we let y = lnx, we then know that x = e^y. By differentiating both sides of this equation with respect to y we get:dx/dy = e^y, as the exponential function differentiates to itself ...

Take out all common factors, in this case only x. This leaves you with x(1-4x^2).Within the brackets you now have a quadratic equation which you can factorise. You need to find factors of -4x^2 that plus ...

Given this is a maths problem a whiteboard will be heavily relied upon, but I'll do my best to get the appropriate notation here.Starting with y=e^{3x-x^3}, we have to get to the stationary points...

In order to fully understand how differentiation works, it is useful to be able to derive it. To do this, we must first consider the general curve y = f(x), we'll make this curve more specific later on. F...

Suppose y is a function of x: y = f(x) At the maximum/minimum of the curve y, the first derivative of the function (with respect to x) is equal to zero:dy/dx = 0To check ...