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

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

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

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

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

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

Solution steps

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

Apply the chain rule:

\frac{1}{3 x + 1} \frac{d}{d x} (3 x + 1)

= \frac{1}{3 x + 1} \frac{d}{d x} (3 x + 1)

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

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

Simplify

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

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

(x^{3} (8 - 3 x))^{^{'}}

\int (ln (x)) d x

\int \frac{3 e ^{x}}{1 - e ^{x}} d x

x = y (y - 3), x = - y (y - 3)

\int - 20 t^{\frac{2}{3}} - 70 d t

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