What is the derivative of \sqrt[5]{x}+4sqrt(x^5) ?

The derivative of \sqrt[5]{x}+4sqrt(x^5) is (1+50x^{23/10})/(5x^{4/5)}

What is the first derivative of \sqrt[5]{x}+4sqrt(x^5) ?

The first derivative of \sqrt[5]{x}+4sqrt(x^5) is (1+50x^{23/10})/(5x^{4/5)}

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derivative

\frac{1 + 50 x ^{\frac{23}{10}}}{5 x ^{\frac{4}{5}}}

Solution steps

\frac{d}{d x} (5 x + 4 x^{5})

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (5 x) + \frac{d}{d x} (4 x^{5})

\frac{d}{d x} (5 x) = \frac{1}{5 x ^{\frac{4}{5}}}

\frac{d}{d x} (4 x^{5}) = 10 x^{\frac{3}{2}}

= \frac{1}{5 x ^{\frac{4}{5}}} + 10 x^{\frac{3}{2}}

Simplify

\frac{1}{5 x ^{\frac{4}{5}}} + 10 x^{\frac{3}{2}} : \frac{1 + 50 x ^{\frac{23}{10}}}{5 x ^{\frac{4}{5}}}

= \frac{1 + 50 x ^{\frac{23}{10}}}{5 x ^{\frac{4}{5}}}

What is the derivative of \sqrt[5]{x}+4sqrt(x^5) ?
The derivative of \sqrt[5]{x}+4sqrt(x^5) is (1+50x^{23/10})/(5x^{4/5)}
What is the first derivative of \sqrt[5]{x}+4sqrt(x^5) ?
The first derivative of \sqrt[5]{x}+4sqrt(x^5) is (1+50x^{23/10})/(5x^{4/5)}