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How you should approach a question of this type in an exam
Say you are given two lines: L₁ and L₂ with equations and you are asked to deduce whether or not they...

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*...

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 ...