Differentiation
GCE Further Mathematics

A curve is defined by the equation y = x³ - 6x² + 9x + 2. (a) Find dy/dx. (b) Determine the coordinates of the stationary points of the curve. (c) Distinguish between the stationary points, stating wh…

Given that y = (3x + 2)⁴(x² - 1), (a) Find dy/dx, simplifying your answer as far as possible. (b) Hence, find the values of x for which dy/dx = 0. (c) A particle moves along a straight line such that …

The gradient of the curve $y = 2x^3 - 9x^2 + 12x - 4$ at the point where $x = 1$ is

The gradient of the curve $y = 2x^3 - 9x^2 + 12x - 4$ at the point where $x = 2$ is

Differentiate $y = (3x + 5)^4$ with respect to $x$.

Find the derivative of y = 5x³ - 3x² + 7x - 2.

If $y = \frac{x^2 + 1}{x - 1}$, find $\frac{dy}{dx}$.

The displacement of a particle at time $t$ seconds is given by $s = t^3 - 6t^2 + 9t + 4$ metres. The particle is momentarily at rest when $t$ equals

Find the coordinates of the stationary point of the curve $y = x^2 - 4x + 7$.

Find the derivative of $y = x^2 \sin x$.

If $f(x) = \frac{3x^2 - 1}{x}$, find $f'(x)$.