Differentiating standard functionsEdexcel A-Level Maths: Flashcards

What these 13 flashcards ask

\frac{d}{dx}\left(e^{kx}\right)
\frac{d}{dx}\left(a^{kx}\right)
\frac{d}{dx}(\ln x)
\frac{d}{dx}(\sin kx)
\frac{d}{dx}(\cos kx)
\frac{d}{dx}(\tan kx)
Why must x be in radians for the trig derivatives?
Derivative of 5^{2x}?
Derivative of 3\ln x?
First principles: chord gradient from x to x+h?
Identity used to find \frac{d}{dx}\sin x from first principles?
Small-angle approximations used as h\to0?
Gradient of y=e^{3x}+\sin2x at x=0?

Exam questions on Differentiating standard functions

A curve has equation $y=e^{3x}+\sin 2x$ , where $x$ is in radians.
Find the equation of the tangent to the curve at the point where $x=0$ .2 marks
The function $f$ is defined by $f(x)=5^{2x}$ for all real $x$ .
Find the exact value of $x$ for which $f'(x)=50\ln5$ .2 marks
The curve $y=\sin x$ (with $x$ in radians) has a point $P$ with $x$ -coordinate $x$ . A point $Q$ on the curve has $x$ -coordinate $x+h$ , where $h$ is small and non-zero.
Show that the gradient of the chord $PQ$ is $\sin x\left(\frac{\cos h-1}{h}\right)+\cos x\left(\frac{\sin h}{h}\right)$ .3 marks

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).