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9(iii)   Find the derivative of x ^{-3} ( 5 + 3x ) 

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Given

f(x)=x ^{-3} ( 5 + 3x )=5x^{-3}+3x^{-2}

As we know, the property,

f'(x^n)=nx^{n-1}

and the property 

\frac{d(y_1+y_2)}{dx}=\frac{dy_1}{dx}+\frac{dy_2}{dx}

applying that property we get

f'(x)=(-3)5x^{-4}+3(-2)x^{-3}

f'(x)=-15x^{-4}-6x^{-3}

 

Posted by

Pankaj Sanodiya

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