\frac{d}{dx}(\ln kx)?

\frac1x (the constant k drops out).

Differentiating exponential, logarithmic and trigonometric functionsEdexcel International A Level Maths: Flashcards

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$\frac{d}{dx}\left(e^{kx}\right)$?

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$\frac{d}{dx}\left(e^{kx}\right)$ ?: $ke^{kx}$ .
$\frac{d}{dx}(\ln x)$ ?: $\frac1x$ .
$\frac{d}{dx}(\ln kx)$ ?: $\frac1x$ (the constant $k$ drops out).
$\frac{d}{dx}(\sin kx)$ ?: $k\cos kx$ .
$\frac{d}{dx}(\cos kx)$ ?: $-k\sin kx$ .
$\frac{d}{dx}(\tan kx)$ ?: $k\sec^{2}kx$ .
$\frac{d}{dx}(a^{x})$ ?: $a^{x}\ln a$ .
$\frac{d}{dx}(3e^{4x}-\sin2x)$ ?: $12e^{4x}-2\cos2x$ .
Units needed for trigonometric differentiation?: Radians.
What is $\sec x$ ?: $\frac{1}{\cos x}$ .
Condition for a stationary point?: $\frac{dy}{dx}=0$ .
Equation of the tangent at $(x_1,y_1)$ with gradient $m$ ?: $y-y_1=m(x-x_1)$ .

Exam questions on Differentiating exponential, logarithmic and trigonometric functions

The curve $C_1$ has equation $y=5e^{2x}-\ln3x$ for $x>0$ .
Find $\dfrac{d^{2}y}{dx^{2}}$ .2 marks
The curve $C_2$ has equation $y=4\sin3x+\cos2x$ , where $x$ is in radians.
Find $\dfrac{d^{2}y}{dx^{2}}$ .2 marks
The curve $C_3$ has equation $y=2^{x}$ .
Find the gradient of $C_3$ at $x=3$ , giving your answer in exact form and to 3 significant figures.3 marks

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Written by the Exaim team, led by Shaun Daswani (Head of Upper Secondary, Improve ME Institute; MSc Financial Mathematics, Imperial College London; BSc, UCL) and Jason Daswani (operational lead, Improve ME Institute; LSE).