What is the derivative of \sqrt[7]{x}+4sqrt(x^7) ?

The derivative of \sqrt[7]{x}+4sqrt(x^7) is (1+98x^{47/14})/(7x^{6/7)}

What is the first derivative of \sqrt[7]{x}+4sqrt(x^7) ?

The first derivative of \sqrt[7]{x}+4sqrt(x^7) is (1+98x^{47/14})/(7x^{6/7)}

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\frac{1 + 98 x ^{\frac{47}{14}}}{7 x ^{\frac{6}{7}}}

Solution steps

Apply the Sum/Difference Rule:

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

\frac{d}{d x} (4 x^{7}) = 14 x^{\frac{5}{2}}

= \frac{1}{7 x ^{\frac{6}{7}}} + 14 x^{\frac{5}{2}}

Simplify

\frac{1}{7 x ^{\frac{6}{7}}} + 14 x^{\frac{5}{2}} : \frac{1 + 98 x ^{\frac{47}{14}}}{7 x ^{\frac{6}{7}}}

= \frac{1 + 98 x ^{\frac{47}{14}}}{7 x ^{\frac{6}{7}}}

What is the derivative of \sqrt[7]{x}+4sqrt(x^7) ?
The derivative of \sqrt[7]{x}+4sqrt(x^7) is (1+98x^{47/14})/(7x^{6/7)}
What is the first derivative of \sqrt[7]{x}+4sqrt(x^7) ?
The first derivative of \sqrt[7]{x}+4sqrt(x^7) is (1+98x^{47/14})/(7x^{6/7)}