3.6.6 Differentiation (A-level only)

The curve $C$ has equation

3y^{2} + 2xy^{2} = 12(3^{x}) + 15, \quad y > 0

a.

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

[6]

b.

Curve $C$ cuts the $y$ -axis at the point $P$ .

Find the exact value of the gradient of the tangent to $C$ at $P$ .

[4]

The curve $C$ has equation

3y^{2} + 2xy^{2} = 12(3^{x}) + 15, \quad y > 0

a.

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

[6]

b.

Curve $C$ cuts the $y$ -axis at the point $P$ .

Find the exact value of the gradient of the tangent to $C$ at $P$ .

[4]

3.6.6 Differentiation (A-level only) Questions