1.9.16 Implicit differentiation (A-level only)

A curve has equation

5y^2 + 2x = 5ye^{-3x}

a.

Find $dydx\frac{dy}{dx}$ in terms of $x$ and $y$ .

[4]

b.

The curve crosses the $y$ -axis at the origin and at the point $P$ .

Find the equation of the normal to the curve at $P$ , writing your answer in the form $y = m x + c$ where $m$ and $c$ are constants to be found.

[5]

A curve has equation

5y^2 + 2x = 5ye^{-3x}

a.

Find $dydx\frac{dy}{dx}$ in terms of $x$ and $y$ .

[4]

b.

The curve crosses the $y$ -axis at the origin and at the point $P$ .

Find the equation of the normal to the curve at $P$ , writing your answer in the form $y = m x + c$ where $m$ and $c$ are constants to be found.

[5]

1.9.16 Implicit differentiation (A-level only) Questions