Product, quotient and chain rulesEdexcel A-Level Maths: Mind map

Exam questions on Product, quotient and chain rules

1. 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
2. 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
3. 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