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

The derivative of \sqrt[5]{x^2+ln(x^2}) is (2x^2+2)/(5x(x^2+2ln(x))^{4/5)}

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

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

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\frac{2 x ^{2} + 2}{5 x ( x ^{2} + 2 ln ( x ) ) ^{\frac{4}{5}}}

Solution steps

Apply the chain rule:

\frac{1}{5 ( x ^{2} + ln ( x ^{2} ) ) ^{\frac{4}{5}}} \frac{d}{d x} (x^{2} + ln (x^{2}))

= \frac{1}{5 ( x ^{2} + ln ( x ^{2} ) ) ^{\frac{4}{5}}} \frac{d}{d x} (x^{2} + ln (x^{2}))

\frac{d}{d x} (x^{2} + ln (x^{2})) = 2 x + \frac{2}{x}

= \frac{1}{5 ( x ^{2} + ln ( x ^{2} ) ) ^{\frac{4}{5}}} (2 x + \frac{2}{x})

Simplify

\frac{1}{5 ( x ^{2} + ln ( x ^{2} ) ) ^{\frac{4}{5}}} (2 x + \frac{2}{x}) : \frac{2 x ^{2} + 2}{5 x ( x ^{2} + 2 ln ( x ) ) ^{\frac{4}{5}}}

= \frac{2 x ^{2} + 2}{5 x ( x ^{2} + 2 ln ( x ) ) ^{\frac{4}{5}}}

\frac{1}{x - 1}

\int \frac{8 z ^{2} + 2}{2 z ^{3} + z}

\frac{d}{d x} (\frac{e ^{x} cos ( x )}{e ^{x} - 1})

\frac{d}{d t} (4 cos (2 t))

\frac{d y}{d x} = (\frac{y}{y - x})

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