Differentiation

WMA13Topic 3.43 questions

Chain, product and quotient rules, and differentiating exponential, log and trig functions.

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Original practice questions written in the style of the exam.

3x

+

3x2e3x

M1 Sets

\dfrac{dy}{dx} = 0

and factorises:

xe^{3x}(2 + 3x) = 0

, noting

e^{3x} \neq 0

(1)

A1

x = 0

and

x = -\tfrac{2}{3}

(1)

A1

(0, 0)

and

\left(-\tfrac{2}{3}, \dfrac{4}{9e^2}\right)

(1)

(a) Show that $\dfrac{dy}{dx} = \dfrac{2\cos x + 1}{(2 + \cos x)^2}$ .

(b) Find the value of $x$ in the interval $0 < x < \pi$ at which $C$ has a stationary point.

Mark scheme