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I would start by asking the student the different forms of integration we know (e.g. substitution, parts).I would then ask the student whether parts or substitution gives the easiest method.If the student is...

In order to answer this question you need to use integration by parts.Using the standard integration by parts formula: ∫u dv/dx dx = uv-∫v du/dx dx.Let:u=ln(x) v=(1/2)x 2 du/dx=1/x dv/dx=xTherefore we get:I=...

Implicit differentiation is used when the function you need to differentiate is not in the form y = f(x). For example: y 4 + 3x 2 - 10 + 2y 2 = 4xThe first step is to differentiate each term of the equation ...

f(x) = x 4 - 4x 3 + 4x 2 Given the function above, we need to find its stationary points. Its stationary points occur either at the minima and maxima of the function or at the endpoints. Noticing that the do...

The derivative of a function describes the gradient, also known as the slope. In the simplest terms, the slope defines the change in y divided by the change in x. So if there is a large increase in y for a s...