Course home

9.8 Implicit Differentiation

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46

Question 23

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]

Markscheme

9.8 Implicit Differentiation Questions

A Level
Maths
9.8 Implicit Differentiation

47 exam-style questions on Edexcel A Level Maths 9.8 Implicit Differentiation. Each one has a worked solution and a mark scheme showing where the marks go.

9.8 Implicit Differentiation

Question bank

9.8 Implicit Differentiation

Medium Hard

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46

Question 23

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]

Markscheme

9.8 Implicit Differentiation Questions

A Level
Maths
9.8 Implicit Differentiation

47 exam-style questions on Edexcel A Level Maths 9.8 Implicit Differentiation. Each one has a worked solution and a mark scheme showing where the marks go.