Let #160;u=x5; #160;v=3 6x 9Then, #160;u #39;=5x4; #160;v #39;=54x 10Using #160;the #160;product #160;rule:ddxuv=uv #39;+vu #39;ddxx53 6x ...

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Properties of Inequalities

x53-6 x-9

Question

x⁵ (3 − 6x⁻⁹)

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Solution

$Let u = x^{5}; v = (3 - 6 x^{- 9}) Then, u' = 5 x^{4}; v' = 54 x^{- 10} Using the product rule: \frac{d}{d x} (u v) = u v' + v u' \frac{d}{d x} [x^{5} (3 - 6 x^{- 9})] = x^{5} (54 x^{- 10}) + (3 - 6 x^{- 9}) (5 x^{4}) = 54 x^{- 5} + 15 x^{4} - 30 x^{- 5} = 15 x^{4} + 24 x^{- 5}$

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Similar questions

x^{5} (3 - 6 x^{- 9})

x^{5} (3 - 6 x^{- 9})

Find the derivative of:

(i) 2x - $\frac{3}{4}$
(ii) $(5 x^{3} + 3 x - 1)$ (x-1)

(iii) $x^{- 3}$ (5+3x)
(iv) $x^{5} (3 - 6 x^{- 9})$

(v) $x^{- 4} (3 - 4 x^{- 5})$
(vi) $\frac{2}{x + 1} - \frac{x^{2}}{3 x - 1}$

Find the derivative of

(i) (ii) (5x³ + 3x – 1) (x – 1)

(iii) x^–3 (5 + 3x) (iv) x⁵ (3 – 6x^–9)

(v) x^–4 (3 – 4x^–5) (vi)

\int {(\frac{x}{1 + x^{5}})}^{3 / 2} d x

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