A-Level CAIE Mathematics A2 3.4 Differentiation Question Bank

Find the exact coordinates of the points on the curve $y=\frac{x^{2}}{1-3 x}$ at which the gradient of the tangent is equal to 8 .

The parametric equations of a curve are

Find the gradient of the curve at the point for which t=0.

The curve $y=\frac{\ln x}{x^{3}}$ has one stationary point. Find the x-coordinate of this point.

Find the exact coordinates of the stationary point on the curve with equation $y=5 x \mathrm{e}^{\frac{1}{2} x}$.

The parametric equations of a curve are

Find $\frac{\mathrm{d} y}{\mathrm{~d} x}$ in terms of t, simplifying your answer as far as possible.

The equation of a curve is $y=\frac{\mathrm{e}^{2 x}}{1+\mathrm{e}^{2 x}}$. Show that the gradient of the curve at the point for which $x=\ln 3$ is $\frac{9}{50}$.

Find $\frac{\mathrm{d} y}{\mathrm{~d} x}$ in each of the following cases:

Find the exact coordinates of the stationary point of the curve $y=\mathrm{e}^{2 x} \sin 2 x$ for $0 \leqslant x \leqslant \frac{1}{2} \pi$ ．

The parametric equations of a curve are

Show that $\frac{\mathrm{d} y}{\mathrm{~d} x}=\operatorname{cosec} 2 t$.

The equation of a curve is $\cos 3 x+5 \sin y=3$.
Find the gradient of the curve at the point $\left(\frac{1}{9} \pi, \frac{1}{6} \pi\right)$.