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First we must find the gradient of the curve at the point (1, 4) - we do this by finding the derivative dy/dx, as we do to find any gradient. Differentiating the equation of the curve gives us that dy/dx ...

The aim of this maths question is to find the two unknowns, x and y, by using simultaneous equations. Simultaneous equations can be solved by either using the elimination method or the substitution method...

Integrating by parts requirez recognition that ln(x) is equal to ln(x) multiplied by 1. Making u equal to ln(x) should make the integration trivial. Differentiation is a simple use of the product rule and...

The equation looks horrible to start so we need to tidy it up. We do this by firstly getting rid of the fraction. This means that we need to multiply everything else by the denominator (which in this case...

First, let's make y the subject of the equation.

Let's achieve this by having only y on the left hand side of the equation. To do this we need to minus 3x from both sides of the equation. This leav...