1.9.16 Implicit differentiation (A-level only)

A curve $C$ has equation

x^{\cos x} \quad x > 0, \quad y > 0

a.

Find, by firstly taking natural logarithms, an expression for $dydx\frac{dy}{dx}$ in terms of $x$ and $y$ .

[4]

b.

Hence show that the $x$ -coordinates of the stationary points of $C$ are solutions of the equation

\sin(x) \cdot x \ln x = \cos x

[3]

A curve $C$ has equation

x^{\cos x} \quad x > 0, \quad y > 0

a.

Find, by firstly taking natural logarithms, an expression for $dydx\frac{dy}{dx}$ in terms of $x$ and $y$ .

[4]

b.

Hence show that the $x$ -coordinates of the stationary points of $C$ are solutions of the equation

\sin(x) \cdot x \ln x = \cos x

[3]

1.9.16 Implicit differentiation (A-level only) Questions