Product, quotient and chain rulesEdexcel A-Level Maths: Flashcards

What these 13 flashcards ask

Chain rule?
Product rule?
Quotient rule?
\frac{d}{dx}(\sec x)
\frac{d}{dx}(\operatorname{cosec}x)
\frac{d}{dx}(\cot x)
Derivative of \cos^{2}x?
Derivative of \tan^{2}2x?
Derivative of 2x^{4}\sin x?
Derivative of \frac{e^{3x}}{x}?
Link between \frac{dy}{dx} and \frac{dx}{dy}?
How do you connect \frac{dV}{dt} to \frac{dr}{dt}?
If x=3\tan2y, what is \frac{dx}{dy}?

Exam questions on Product, quotient and chain rules

The function $f$ is defined by $f(x)=x^{3}e^{2x}$ for all real $x$ .
Find the equation of the tangent to the curve $y=f(x)$ at the point where $x=1$ .2 marks
The function $h$ is defined by $h(x)=\frac{\ln x}{x^{2}}$ for $x>0$ .
Find the exact value of $h(x)$ at the stationary point.2 marks
A spherical balloon is inflated so that its volume, $V$ cm $^3$ , increases at a constant rate of $200$ cm $^3$ s $^{-1}$ . The radius of the balloon is $r$ cm. The volume of a sphere is $V=\frac43\pi r^{3}$ and its surface area is $S=4\pi r^{2}$ .
Find the exact rate of increase of the radius when $r=5$ .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).