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Popular >

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

Solution

derivative of

Solution

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

Solution steps

Apply the chain rule:

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

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

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

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

Simplify

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

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

Popular Examples

limit as x approaches 0 of 1/(2+3^{1/x)}

x \to 0 lim (\frac{1}{2 + 3 ^{\frac{1}{x}}})

sum from n=1 to infinity of 1/((n+1))

n = 1 \sum \infty \frac{1}{( n + 1 )}

sum from n=0 to infinity of (-1/2)^n

n = 0 \sum \infty (- \frac{1}{2})^{n}

(\partial)/(\partial y)(2xy^3)

\frac{\partial}{\partial y} (2 x y^{3})

y^{''}-8y^'+16y=2te^{4t}

y^{^{''}} - 8 y^{^{'}} + 16 y = 2 t e^{4 t}

Frequently Asked Questions (FAQ)

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