Differentiating inverse functions and implicit relationshipsEdexcel International A Level Maths: Mind map

Exam questions on Differentiating inverse functions and implicit relationships

1. 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
2. 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
3. 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