Differentiation | CIE AS Maths: Pure 1 Topic Questions 2020

1

3 marks

Differentiate

(i)

5 x,

(ii)

2 x^{3}

(iii)

x^{\frac{1}{2}}

.

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1a

2 marks

For each of the following, find $\frac{d y}{d x}$ in terms of $x$ :

$y = - 3 x^{3} + 5 x^{2} - 3 x + \sqrt{13}$

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1b

2 marks

$y = {9 x}^{\frac{1}{3}} - 6 x^{- \frac{1}{3}}$

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1a

1 mark

For each of the following, find $\frac{d y}{d x}$ in terms of $x$ :

$y = 4 x^{2} - 3 x + 19$

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1b

2 marks

$y = x^{3} - 5 x^{2} + 14 x - 1$

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1c

2 marks

$y = {4 x}^{\frac{3}{2}} - {3 x}^{- 1}$

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1a

2 marks

For each of the following, find $\frac{d y}{d x}$ in terms of $x$ :

$y = - \frac{5}{4} x^{3} + \frac{3}{5} x^{2} - x \sqrt{2} + π$

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1b

2 marks

$y = \frac{3}{2} x^{\frac{4}{5}} - \frac{10}{3} x^{- \frac{4}{5}}$

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CIE AS Maths: Pure 1