Question Bank

Differentiate $f(x)=\sqrt{(4-9x^4)}$.

*You do not need to simplify your answer.*

A curve is defined by the equation $y=(x^2+3x+2)\sin x$.

Find the gradient of the tangent to this curve when $x=0$.

*You must use calculus and show any derivatives that you need to find when solving this problem.*

A function is defined parametrically by the pair of equations:

$x=3t^2+1$ and $y=\cos t.$

Find an expression for $\frac{\mathrm{d}y}{\mathrm{d}x}$.

An object is travelling in a straight line. Its displacement, in metres, is given by the formula

$s(t)=\ln (3t^2+5t+2)$, where $t>0$ and $t$ is time, in seconds.

Find the velocity of this object when $t=1$ second.

*You must use calculus and show any derivatives that you need to find when solving this problem.*

Differentiate $y=\sqrt{x}.\sec (6x)$.

You do not need to simplify your answer.

Differentiate $y=\sqrt{3x-2}$.

*You do not need to simplify your answer.*

Find the rate of change of the function $f(t)=t^2{e}^{2t}$ when $t=1.5$.

You must use calculus and show any derivatives that you need to find when solving this problem.

Differentiate $f(x)=\frac{x^2}{\cos x}$.

*You do not need to simplify your answer.*

Find the gradient of the tangent to the curve $y=\cot (2x)$ at the point where $x=\frac{\pi }{12}$.

You must use calculus and show any derivatives that you need to find when solving this problem.

Differentiate $y=\ln (x^2-x^4+1)$.

*You do not need to simplify your answer.*