What is the derivative of (12/(x^5)-7/(\sqrt[5]{x)}) ?

The derivative of (12/(x^5)-7/(\sqrt[5]{x)}) is (-300x^{6/5}+7x^6)/(5x^{36/5)}

What is the first derivative of (12/(x^5)-7/(\sqrt[5]{x)}) ?

The first derivative of (12/(x^5)-7/(\sqrt[5]{x)}) is (-300x^{6/5}+7x^6)/(5x^{36/5)}

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\frac{- 300 x ^{\frac{6}{5}} + 7 x ^{6}}{5 x ^{\frac{36}{5}}}

Solution steps

Apply the Sum/Difference Rule:

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

\frac{d}{d x} (\frac{12}{x ^{5}}) = - \frac{60}{x ^{6}}

= - \frac{60}{x ^{6}} - (- \frac{7}{5 x ^{\frac{6}{5}}})

Simplify

- \frac{60}{x ^{6}} - (- \frac{7}{5 x ^{\frac{6}{5}}}) : \frac{- 300 x ^{\frac{6}{5}} + 7 x ^{6}}{5 x ^{\frac{36}{5}}}

= \frac{- 300 x ^{\frac{6}{5}} + 7 x ^{6}}{5 x ^{\frac{36}{5}}}

What is the derivative of (12/(x^5)-7/(\sqrt[5]{x)}) ?
The derivative of (12/(x^5)-7/(\sqrt[5]{x)}) is (-300x^{6/5}+7x^6)/(5x^{36/5)}
What is the first derivative of (12/(x^5)-7/(\sqrt[5]{x)}) ?
The first derivative of (12/(x^5)-7/(\sqrt[5]{x)}) is (-300x^{6/5}+7x^6)/(5x^{36/5)}