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Popular >

derivative of ln(x^{1/3})

Solution

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

Solution

\frac{1}{3 x}

Solution steps

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

Apply the chain rule:

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

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

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

= \frac{1}{x ^{\frac{1}{3}}} \cdot \frac{1}{3 x ^{\frac{2}{3}}}

Simplify

\frac{1}{x ^{\frac{1}{3}}} \cdot \frac{1}{3 x ^{\frac{2}{3}}} : \frac{1}{3 x}

= \frac{1}{3 x}

Popular Examples

derivative of cos(x(1+sin(x)^{10}))

\frac{d}{d x} (cos (x (1 + sin (x))^{10}))

derivative of (x-8/(x^2-4))

\frac{d}{d x} (\frac{x - 8}{x ^{2} - 4})

slope of x^2+xy-y^2=3,(5,3)slope

x^{2} + x y - y^{2} = 3, (5, 3)

inverse oflaplace 1/(s^2-6s+10)inverse laplace

\frac{1}{s ^{2} - 6 s + 10}

f(x)=2cos(x^3)-2/x

f (x) = 2 cos (x^{3}) - \frac{2}{x}

Frequently Asked Questions (FAQ)

What is the derivative of ln(x^{1/3}) ?
The derivative of ln(x^{1/3}) is 1/(3x)
What is the first derivative of ln(x^{1/3}) ?
The first derivative of ln(x^{1/3}) is 1/(3x)