Differentiating inverse functions and implicit relationshipsEdexcel International A Level Maths: Flashcards

What these 12 flashcards ask

State the rule for \frac{dy}{dx} when x is a function of y.
When does \frac{dy}{dx}=\frac{1}{dx/dy} fail?
x=\sin 3y: find \frac{dx}{dy}.
x=\sin 3y: find \frac{dy}{dx}.
x=\cos 2y: find \frac{dy}{dx}.
x=\tan y: find \frac{dy}{dx} in terms of x.
x=e^{3y}: find \frac{dy}{dx} in terms of x.
x=\ln y: find \frac{dy}{dx}.
Identity used to write \sec^2 2y in terms of x=\tan 2y?
x=y^3+y: find \frac{dy}{dx} at y=1.
Gradient of a normal if the tangent gradient is \frac18?
To find the gradient at a point on x=f(y), which coordinate is substituted?

Exam questions on Differentiating inverse functions and implicit relationships

A curve $C$ has equation $x=\sin 3y$ for $-\frac{\pi}{6}<y<\frac{\pi}{6}$ .
Find the exact value of $\frac{dy}{dx}$ at the point where $y=\frac{\pi}{18}$ .2 marks
A curve $C$ has equation $x=e^{2y}+y$ .
Find an equation of the tangent to $C$ at the point where $y=0$ .2 marks
A curve $C$ has equation $x=\tan 2y$ for $-\frac{\pi}{4}<y<\frac{\pi}{4}$ .
Show that $\frac{dy}{dx}=\frac{1}{2(1+x^2)}$ .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).