The curve $C\,$ has equation

2\sec^2 3y, \quad x > 2, \quad 0 < y < \frac{\pi}{6}

Find $dxdy\displaystyle \frac{\text{d}x}{\text{d}y}$ in terms of $y$ .

Hence show that

\frac{\text{d}y}{\text{d}x} = \frac{p}{qx\sqrt{x-2}}

where $p\,$ is irrational and $q\,$ is an integer, stating the values of $p\,$ and $q$ .

Find the equation of the normal to $C\,$ at the point where $y=π18\displaystyle y = \frac{\pi}{18}$ , giving your answer in the form $y = m x + c$ where $m\,$ and $c\,$ are exact constants.

The curve $C\,$ has equation

2\sec^2 3y, \quad x > 2, \quad 0 < y < \frac{\pi}{6}

Find $dxdy\displaystyle \frac{\text{d}x}{\text{d}y}$ in terms of $y$ .

Hence show that

\frac{\text{d}y}{\text{d}x} = \frac{p}{qx\sqrt{x-2}}

where $p\,$ is irrational and $q\,$ is an integer, stating the values of $p\,$ and $q$ .

Find the equation of the normal to $C\,$ at the point where $y=π18\displaystyle y = \frac{\pi}{18}$ , giving your answer in the form $y = m x + c$ where $m\,$ and $c\,$ are exact constants.

Differentiation

Question 562

Markscheme

Differentiation

Question 562

Markscheme

Differentiation

Question 562

Differentiation Questions

Differentiation

Question 562

Differentiation Questions