Differentiation (AQA GCSE Further Maths): Exam Questions

$y=2x^{10}-\frac{3}{x^2}$

Work out $\frac{\mathrm{d}y}{\mathrm{d}x}$.

$y=\frac{2x^7+15x^2}{3x}$

Work out the value of $x$ when $\frac{\mathrm{d}y}{\mathrm{d}x}=133$.

For the curve   $y=\mathrm{f}\left(x\right)$,

$\frac{dy}{dx}=\frac{3}{2}x-k{x}^4+k$   where $k$ is a constant.

When $x=-2$ the gradient of the curve is 12.

Work out the value of $k$.

A curve has the equation $y=x^3+a{x}^2-7$ where a is a constant.

The gradient of the curve when $x=4$ is twice the gradient of the curve when$x=-1$

Work out the value of $a$. You must show your working.

$y=x^3+3x^2-40x-7$

Find the two values of $x$ for which the rate of change of $y$ with respect to $x$ is $5$.

$v=\frac{{\left(2t^3-1\right)}^2}{3t^7}$

Find the rate of change of $v$ with respect to $t$ at the point when $t=0.5$

$y=p{x}^4+q{x}^{-4}+2$ is the equation of a curve, where $p$ and $q$ are integers.

You are given that $\frac{\mathrm{d}y}{\mathrm{d}x}=\frac{28x^8+12}{x^5}$.

Find the values of $p$ and $q$.

A curve has the equation

$y=x^n+b{x}^3+c$

where $n$ is a positive integer greater than 1, and $b$ and $c$ are integers.

The curve has a $y$-intercept of $-5$.

The curve passes through the point $\left(1,8\right)$, at which the gradient of the curve is $45$.

Find the values of $n$, $b$ and $c$.