A-level · Differentiation

Differentiating exponentials and logarithmsExam-style questions

The functions whose rate of change is proportional to their size. Why the gradient of any exponential is its height times a constant; the base e, which makes that constant exactly 1; e^(kx) with the chain rule; other bases and their factor of ln a; the derivative of ln x and of ln of anything; and exponentials and logs with the product and quotient rules.

Start practising Read the lesson

19 questions · A-level level · mark scheme and worked solution on each · no sign-up to try

DifficultyAll Level 2 Level 3 Level 4 Level 5

1
The curve $C$ has equation $y = 4\ln(3 - 3\sin x)$ , where $x$ is in radians.
(a) Find, in terms of $\pi$ , all the values of $x$ for which $y$ is undefined.

(2 marks)
(b) Determine the exact coordinates of the first stationary point on $C$ to the right of the $y$ -axis.

(4 marks)
(c) (i) Show that $\dfrac{d^2y}{dx^2} + 12e^{-\frac14 y} = 0$ .

(ii) Using the result in part (c)(i), state, with a reason, whether the stationary points of $C$ are maxima or minima.

(6 marks)
Level 5 · 12 marksTry it