Differentiating exponentials, logarithms and trigonometric functionsAQA A-Level Maths: Mind map

Exam questions on Differentiating exponentials, logarithms and trigonometric functions

1. A curve has equation $y=e^{3x}-4x$.
   Find the exact $x$-coordinate of the stationary point of the curve.2 marks
2. A curve has equation $y=\tan2x$ for $-\frac{\pi}{4}<x<\frac{\pi}{4}$, where $x$ is in radians.
   Find the equation of the tangent to the curve at $x=\frac{\pi}{8}$.2 marks
3. The population $P$ of a colony of bacteria, in thousands, is modelled by $P=5\times2^{0.4t}$, where $t$ is the time in hours after the colony is first observed.
   Find $\frac{dP}{dt}$ in terms of $t$.3 marks