What is the derivative of \sqrt[4]{x^5}-3/(x^2) ?

The derivative of \sqrt[4]{x^5}-3/(x^2) is (5x^{13/4}+24)/(4x^3)

What is the first derivative of \sqrt[4]{x^5}-3/(x^2) ?

The first derivative of \sqrt[4]{x^5}-3/(x^2) is (5x^{13/4}+24)/(4x^3)

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\frac{5 x ^{\frac{13}{4}} + 24}{4 x ^{3}}

Solution steps

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

\frac{d}{d x} (\frac{3}{x ^{2}}) = - \frac{6}{x ^{3}}

= \frac{5 x ^{\frac{1}{4}}}{4} - (- \frac{6}{x ^{3}})

Simplify

\frac{5 x ^{\frac{1}{4}}}{4} - (- \frac{6}{x ^{3}}) : \frac{5 x ^{\frac{13}{4}} + 24}{4 x ^{3}}

= \frac{5 x ^{\frac{13}{4}} + 24}{4 x ^{3}}

What is the derivative of \sqrt[4]{x^5}-3/(x^2) ?
The derivative of \sqrt[4]{x^5}-3/(x^2) is (5x^{13/4}+24)/(4x^3)
What is the first derivative of \sqrt[4]{x^5}-3/(x^2) ?
The first derivative of \sqrt[4]{x^5}-3/(x^2) is (5x^{13/4}+24)/(4x^3)