CAIE A-Level Mathematics AS 1.7.2 Differentiation Rules Questions

Practise differentiating rational powers, sums and composite expressions with the power and chain rules and simplifying first or second derivatives before substitution.

Exam points

Differentiate sums and constant multiples of powers x^n for rational n to obtain first and second derivatives.
Apply the chain rule to composite functions, including powers of linear expressions, and simplify the derivative.
Evaluate a first or second derivative at a specified x-value, including the rate of change of the gradient.

[Maximum number: 2]

The equation of a curve is

y=k \sqrt{4 x+1}-x+5,

where k is a positive constant.

Find $\frac{\mathrm{d} y}{\mathrm{~d} x}$ .

$\frac{\mathrm{d} y}{\mathrm{~d} x}=\left\{k \frac{1}{2}(4 x+1)^{-\frac{1}{2}}\right\}\{\times 4\}\{-1\}$

B2,1,0

OE e.g. $2 k(4 x+1)^{-\frac{1}{2}}-1$

B2 Three correct unsimplified \{ \} and no others.

B1 Two correct $\}$ or three correct $\}$ and an additional term e.g. +5.

B0 More than one error.

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CAIE A-Level Mathematics AS 1.7.2 Differentiation Rules Questions question 1