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Popular >

derivative of ln(x+\sqrt[5]{x^3})

Solution

Solution

\frac{5 x ^{\frac{2}{5}} + 3 x}{5 x ^{\frac{7}{5}}}

Solution steps

Apply the Sum/Difference Rule:

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

\frac{d}{d x} (ln (x)) = \frac{1}{x}

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

Simplify

\frac{1}{x} + \frac{3}{5 x ^{\frac{2}{5}}} : \frac{5 x ^{\frac{2}{5}} + 3 x}{5 x ^{\frac{7}{5}}}

= \frac{5 x ^{\frac{2}{5}} + 3 x}{5 x ^{\frac{7}{5}}}

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Frequently Asked Questions (FAQ)

What is the derivative of ln(x+\sqrt[5]{x^3}) ?
The derivative of ln(x+\sqrt[5]{x^3}) is (5x^{2/5}+3x)/(5x^{7/5)}
What is the first derivative of ln(x+\sqrt[5]{x^3}) ?
The first derivative of ln(x+\sqrt[5]{x^3}) is (5x^{2/5}+3x)/(5x^{7/5)}