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Here we will use:

cot(x) = cos(x)/sin(x)

cosec²(x) = 1 + cot²(x)

Chain rule : dy/dt * dt/ dx = dy/ dx

Product rule : d/dx (...

dy/dx represents the gradient of a curve. The d represents an infinitesimally small range so it is essentially as though you are doing change in y over change in x like you would for a y = mx +c graph ...

Say we have an equation with the product of two subjects in the form f(x) = u(x)v(x).

Differentiating is simple, we would just multiply the differential*...

Take the sequence;

9,    12,    19,    30,    ...

(1) The first step is always to look at difference between the terms;

9,    12,    19,...