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Popular >

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

Solution

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

Solution

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

Solution steps

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

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 )}

Graph

Popular Examples

integral of 4sec^3(x)

\int 4 sec^{3} (x) d x

integral of (3t)/(sqrt(1-9t^4))

\int \frac{3 t}{1 - 9 t ^{4}} d t

integral of 3cos(3x)

\int 3 cos (3 x) d x

tangent of f(x)=5e^x+7x,\at x=0 tangent of

f (x) = 5 e^{x} + 7 x, at x = 0

tangent of f(x)=-3x^2-5x+1,\at x=1 tangent of

f (x) = - 3 x^{2} - 5 x + 1, at x = 1

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)}