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  • Differentiate each of the functions w.r. to x in (x+1/x)^3

Differentiate each of the functions w.r. to x in


\left(x+\frac{1}{x}\right)^{3}

Answers (1)

 

    Let y= \left( x+\frac{1}{x} \right) ^{3} \\ \\ 


 \\ \frac{dy}{dx}=\frac{d}{dx} \left( x+\frac{1}{x} \right) ^{3}=3 \left( x+\frac{1}{x} \right) ^{2} \left( 1-\frac{1}{x^{2}} \right) \\ \\ =3 \left( x^{2}+2+\frac{1}{x^{2}} \right) \left( 1-\frac{1}{x^{2}} \right) \\ \\ =3 \left( x^{2}+2+\frac{1}{x^{2}}-1-\frac{2}{x^{2}}-\frac{1}{x^{4}} \right) \\ \\ =3x^{2}+3-\frac{3}{x^{2}}-\frac{3}{x^{4}} \\ \\

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infoexpert21

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