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

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

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

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

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derivative of

ln (3 \frac{3 x}{x + 2})

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

Solution steps

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

Apply the chain rule:

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

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

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

= \frac{1}{3 \frac{3 x}{x + 2}} \cdot \frac{2}{3 ^{\frac{2}{3}} x ^{\frac{2}{3}} ( x + 2 ) ^{\frac{4}{3}}}

Simplify

\frac{1}{3 \frac{3 x}{x + 2}} \cdot \frac{2}{3 ^{\frac{2}{3}} x ^{\frac{2}{3}} ( x + 2 ) ^{\frac{4}{3}}} : \frac{2}{3 3 \cdot 3 ^{\frac{2}{3}} 3 x x ^{\frac{2}{3}} ( x + 2 )}

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

\int - z^{2} d z

\frac{\partial}{\partial x} (y \cdot e^{\frac{x}{y}})

x \to 0 lim (\frac{sin ( 2 x ) sin ( 3 x )}{sin ( 2 x ) sin ( 3 x )})

\frac{d x}{d t} - 5 x = sin (2 t)

\frac{\partial}{\partial x} (\frac{7 y}{x ^{2} + 7 y ^{2}})

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