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Here we will use: cot(x) = cos(x)/sin(x) cosec 2 (x) = 1 + cot 2 (x) Chain rule : dy/dt * dt/ dx = dy/ dx Product rule : d/dx (u v) = u dv/dx + v*du/dx x = cot(y)= cos(y)/sin(y) dx/dy = -cos(y) ( cos(y) / si...

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 but ov...

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 * of u(x) by v(x) and add the differential of v(x) tim...

Take the sequence; 9, 12, 19, 30, ... (1) The first step is always to look at difference between the terms; 9, 12, 19, 30, ... +3, +7, +11, ... +4, +4, ... We can see the difference is not constant, (2) so w...

So we initially have the relationship y = ln(sin(3x)). As the left hand side is a function of the variable y and the right hand side is a function of the variable x i.e they are implicitly related, we need t...