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The derivative of a function f(x) is a measure of how the function f changes as its variable x changes. You have already met an example of derivatives: the gradient, m,...

Sketching trigonometric graphs is all about working from the graphs you already know and seeing how they behave when added/multiplied/substracted from each other to sketch more complicated functions.

[1 -2; -5 -4] determinant = {1 * (-4)} - {-5 * (-2)} = -4 - 10 = -14

A quadratic equation is an equations of the form:   ax² + bx + c = 0 (1)  where a is not 0. The ways of finding the roots are:  quadratic formula, factorising, substituting, completing the squa...

Integrate dy/dx = 2x/(x²-4).

We can answer this question using integration by substitution, where we set u = something in terms of x.

In this case we are going to set u = x^2<...