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Home  >>  CBSE XI  >>  Math  >>  Limits and Derivatives
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Find the derivative of $ x^{-3}(5+3x)$

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Let $f(x) = x^{-3}(5+3x)$
By Leibnitz product rule
$ f'(x) = x^{-3}\large\frac{d}{dx}$$(5+3x)+(5+3x)\large\frac{d}{dx}$$(x^{-3})$
$ = x^{-3} (0+3)+(5+3x)(-3x^{-3-1})$
$ = x^{-3}(3)+(5+3x)(-3x^{-4})$
$ = 3x^{-3}-15x^{-4}-9x^{-3}$
$ -6x^{-3}-15x^{-4}$
$ -3x^{-3} \bigg( 2 + \large\frac{5}{x} \bigg)$
$ = \large\frac{-3x^{-3}}{x}$$(2x+5)$
$ =  \large\frac{-3}{x^4}$$(5+2x)$

 

answered Apr 9, 2014 by thanvigandhi_1
edited Apr 9, 2014 by thanvigandhi_1
 
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