Pearson Edexcel IAL Mathematics P1.4.2 Differentiating powers of x

Practise differentiating powers of x, roots and reciprocals, then use gradients at given points to form equations or solve for constants.

Exam points

differentiate sums of powers, roots and reciprocal terms into simplest dy/dx form
use a given gradient at x=2^k or a stationary point to solve for an exact constant
turn dy/dx=3 into an algebraic equation and solve exactly without calculator technology

[Maximum number: 3]

\mathrm{f}(x)=10-2 x-\frac{1}{2 \sqrt{x}}-\frac{1}{x^{3}} \quad x>0

Determine $\mathrm{f}^{\prime}(x)$ .

$f^{\prime}(x)=-2+\frac{1}{4} x^{-\frac{3}{2}}+3 x^{-4}$ }

$x^{n} \rightarrow x^{n-1}$ in at least 1 term other than
10

M1

2 of the 3 terms shown correct

A1

All correct

A1

(3)

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P1.4.2 - Differentiating powers of x question 1