What is the derivative of \sqrt[3]{1-x^3+ln(x}) ?

The derivative of \sqrt[3]{1-x^3+ln(x}) is (-3x^3+1)/(3x(1-x^3+ln(x))^{2/3)}

What is the first derivative of \sqrt[3]{1-x^3+ln(x}) ?

The first derivative of \sqrt[3]{1-x^3+ln(x}) is (-3x^3+1)/(3x(1-x^3+ln(x))^{2/3)}

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\frac{- 3 x ^{3} + 1}{3 x ( 1 - x ^{3} + ln ( x ) ) ^{\frac{2}{3}}}

Solution steps

Apply the chain rule:

\frac{1}{3 ( 1 - x ^{3} + ln ( x ) ) ^{\frac{2}{3}}} \frac{d}{d x} (1 - x^{3} + ln (x))

= \frac{1}{3 ( 1 - x ^{3} + ln ( x ) ) ^{\frac{2}{3}}} \frac{d}{d x} (1 - x^{3} + ln (x))

\frac{d}{d x} (1 - x^{3} + ln (x)) = - 3 x^{2} + \frac{1}{x}

= \frac{1}{3 ( 1 - x ^{3} + ln ( x ) ) ^{\frac{2}{3}}} (- 3 x^{2} + \frac{1}{x})

Simplify

\frac{1}{3 ( 1 - x ^{3} + ln ( x ) ) ^{\frac{2}{3}}} (- 3 x^{2} + \frac{1}{x}) : \frac{- 3 x ^{3} + 1}{3 x ( 1 - x ^{3} + ln ( x ) ) ^{\frac{2}{3}}}

= \frac{- 3 x ^{3} + 1}{3 x ( 1 - x ^{3} + ln ( x ) ) ^{\frac{2}{3}}}

What is the derivative of \sqrt[3]{1-x^3+ln(x}) ?
The derivative of \sqrt[3]{1-x^3+ln(x}) is (-3x^3+1)/(3x(1-x^3+ln(x))^{2/3)}
What is the first derivative of \sqrt[3]{1-x^3+ln(x}) ?
The first derivative of \sqrt[3]{1-x^3+ln(x}) is (-3x^3+1)/(3x(1-x^3+ln(x))^{2/3)}