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This question uses a combination of standard differentiation and the product rule. The second part of the equation cos(x)sin(x) is the product of two funtions so the product rule must be used. Product rul...

When solving this quadratic inequality, we should use a three-step approach. The first step is to reformat the inequality to put one side equal to zero, which is the standard format of a quadratic equatio...

The trick here is to use a technique called the difference of squares. If we multiply the top and bottom of the fraction by the conjugate* of the denominator, we can remove any square root terms from the ...

First take natural logs of both sides, giving us: ln(3^x * e^4x) = ln(e⁷).  The RHS can be simplified using the definition of natural logs, so ln(e⁷) = 7.

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The at first can seem very challenging and you won't be able to tackle this question quickly using simple factorisation, which you can often do for many questions. It is best in this case then to use the ...