Edexcel A-Level Mathematics A2 P3.4.1 Differentiating Exp Log and Trig Functions Questions

Practise differentiating exponential, logarithmic and trigonometric functions, including implicit forms, inverse derivatives and model rates.

Exam points

Differentiate sin(kx), cos(kx) or e^{kx} and evaluate a gradient or rate.
Use dx/dy and trig identities to rewrite dy/dx in terms of x.
Differentiate model formulae and use the derivative to solve for a time.
Use logarithmic differentiation for variable powers such as y=x^{sin x}.

[Maximum number: 5]

A curve C has equation

y=x^{\sin x} \quad x>0 \quad y>0

Find, by firstly taking natural logarithms, an expression for $\frac{\mathrm{d} y}{\mathrm{~d} x}$ in terms of x and y.

$y=x^{\sin x}\Rightarrow \ln y=\sin x\ln x$ $\frac1y\frac{dy}{dx}=\frac{\sin x}{x}+\ln x\cos x$ $\frac{dy}{dx}=y\left(\frac{\sin x}{x}+\ln x\cos x\right)$

All question bank results loaded

Edexcel A-Level Mathematics A2 P3.4.1 Differentiating Exp Log and Trig Functions Questions question 1