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At any stationary point, the gradient of a line is zero.
Therefore dy/dx = 0. If we differentiate the equation of the line, and solve this expression we can find the coordinates of the stationary po...

To integrate this function, we must first recognise that ln(x) can be treated as 1 multiplied by ln(x). Using this knowledge, we can apply the 'integration by parts method' to integrate the function.Formu...

Using the chain rule, differentiate the "outside function" and the "inside function", and multiply the two results to get:dy/dx = 4(x-1)^3 * 1 = 4(x-1)^3

We know that dy/dx = (dy/dt) * (dt/dx). Differentiating each of the equations with respect to t gives. dy/dt = sec(t) tan(t) and dx/dt = sec²(t). Since dt/dx = 1 / (dx/dt) we have that dt...

There are three methods to solve these types of silmultaneous equation questions, substitutution, elimination and matrices. In this example we use substitution and elimination.Elimination example.Eq1). 7x...