Find the derivative of x-3 (5 + 3x) - Vidyadip

Question

Find the derivative of x^-3 (5 + 3x)

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Answer

Here f(x) = x^-3(5 + 3x)
$\therefore \;f{\text{'}}(x) = \frac{d}{{dx}}[{x^{ - 3}}(5 + 3x)]$
$ = {x^{ - 3}}\frac{d}{{dx}}(5 + 3x) + (5 + 3x)\frac{d}{{dx}}({x^{ - 3}})$
= x^-3 × 3 + (5 + 3x) × (- 3x)^-4
$ = \frac{3}{{{x^3}}} - \frac{3}{{{x^4}}}(5 + 3x)$
$ = \frac{3}{{{x^3}}}\left[ {1 - \frac{{5 + 3x}}{x}} \right]$$ = \frac{3}{{{x^3}}}\left[ {\frac{{x - 5 - 3x}}{x}} \right] = \frac{{ - 3}}{{{x^4}}}(5 + 2x)$

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