Differentiating inverse trigonometric and hyperbolic functionsEdexcel International A Level Further Maths: Mind map

Exam questions on Differentiating inverse trigonometric and hyperbolic functions

1. Let $y=\operatorname{arsinh}x$, so that $\sinh y=x$.
   Show that $\frac{dy}{dx}=\frac{1}{\sqrt{1+x^2}}$.2 marks
2. The function $f$ is defined by $f(x)=x\arctan x$.
   Show that $f$ has exactly one stationary point.2 marks
3. The curve $C$ has equation $y=\arcsin x+x\sqrt{1-x^2}$ for $-1<x<1$.
   Show that $\frac{dy}{dx}=2\sqrt{1-x^2}$.3 marks