Mathematics 9709 · AS & A Level · Differentiation

Differentiation — practice question

A curve is defined parametrically by $x = t + \cos t$, $y = \ln(1 + \sin t)$, with $-\frac{\pi}{2} < t < \frac{\pi}{2}$.

(a(i))[5]

Show that, using these results, $\frac{dy}{dx} = \sec t$.

(a(ii))[3]

Hence find the $x$-coordinates of the points on the curve where the gradient is $3$. Give your answers to 3 significant figures.

Worked solution & mark scheme

This 8-mark question has a full step-by-step worked solution and mark scheme. One marking point: “State that $\dfrac{dx}{dt}=1-\sin t$.” …