Differentiating hyperbolic functionsEdexcel International A Level Further Maths: Mind map

Exam questions on Differentiating hyperbolic functions

1. The hyperbolic functions are defined by $\sinh x=\frac{e^x-e^{-x}}{2}$, $\cosh x=\frac{e^x+e^{-x}}{2}$ and $\tanh x=\frac{\sinh x}{\cosh x}$, and $\operatorname{sech}x=\frac{1}{\cosh x}$.
   Use the quotient rule to show that $\frac{d}{dx}\left(\tanh x\right)=\operatorname{sech}^2x$.2 marks
2. The curve $C$ has equation $y=x\sinh^2x$.
   Show that $C$ has exactly one stationary point.2 marks
3. The function $f$ is defined by $f(x)=\frac{\cosh2x}{x+1}$ for $x>-1$.
   Find $f'(x)$.3 marks