1.9.16 Implicit differentiation (A-level only)

In a study of harmonic oscillations with variable frequency, the power $P\,$ produced by a generator at time $t\,$ is modeled by the equation

t^{\cos(3t)} \quad t > 1, \quad P > 0

Find, by firstly taking natural logarithms, an expression for $dPdt\frac{dP}{dt}$ in terms of $t$ and $P$ .

[4]

Hence show that the values of $t\,$ for which the power is stationary are solutions of the equation

\ln t \tan(3t) = 1

[3]

1.9.16 Implicit differentiation (A-level only) Questions

In a study of harmonic oscillations with variable frequency, the power $P\,$ produced by a generator at time $t\,$ is modeled by the equation

t^{\cos(3t)} \quad t > 1, \quad P > 0

Find, by firstly taking natural logarithms, an expression for $dPdt\frac{dP}{dt}$ in terms of $t$ and $P$ .

[4]

Hence show that the values of $t\,$ for which the power is stationary are solutions of the equation

\ln t \tan(3t) = 1

[3]