Differentiating powers of xAQA A-Level Maths: Mind map

Exam questions on Differentiating powers of x

1. A curve has equation $y=4x^3-5x^2+7x-9$.
   Find the values of $x$ at which the gradient of the curve is 7.2 marks
2. A curve has equation $y=5\sqrt{x}-\frac{12}{x^3}$, where $x>0$.
   Find the gradient of the curve at the point where $x=4$.2 marks
3. The function $\mathrm{f}$ is defined by $\mathrm{f}(x)=\frac{(x+2)^2}{\sqrt{x}}$, where $x>0$.
   Show that $\mathrm{f}(x)=x^{\frac32}+4x^{\frac12}+4x^{-\frac12}$.3 marks