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Differentiation is defined as the rate of change of a function. Imagine we had a function f(x), which we shall let equal x². We all know what the graph of x² looks like.

First of all, we have to raise to the power of two the first equation and will obtain: p^2 + 5q = 64. 
We have to proceed the same for the second equation and will obtain: p^2 - 3q = 36. 
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Step 1: Rearrange y = arctan(x) as tan(y) = x.

Step 2: Use implicit differentiation to differentiate this with respect to x, which gives us:

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Sin^2(x) cannot be integrated in its current form so you must use trigonometric identities to change sin^2(x) into something else.

Use the formula for cox(2x): cos(2x)=cos(x+x)=cos^2(x)-s...

We start off by drawing attention to the first number in the question, 12. The number can be broken down into multiples by dividing it by the lowest number (that isn't 1): This breakdown is as follows:...