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Popular Calculus >

derivative of 12x^{1/3}

Solution

\frac{d}{d x} (12 x^{\frac{1}{3}})

Solution

\frac{4}{x ^{\frac{2}{3}}}

Solution steps

\frac{d}{d x} (12 x^{\frac{1}{3}})

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= 12 \frac{d}{d x} (x^{\frac{1}{3}})

Apply the Power Rule:

\frac{d}{d x} (x^{a}) = a \cdot x^{a - 1}

= 12 \cdot \frac{1}{3} x^{\frac{1}{3} - 1}

Simplify

12 \cdot \frac{1}{3} x^{\frac{1}{3} - 1} : \frac{4}{x ^{\frac{2}{3}}}

= \frac{4}{x ^{\frac{2}{3}}}

Graph

Popular Examples

(dy)/(dx)= 1/(3x^2y^2)

\frac{d y}{d x} = \frac{1}{3 x ^{2} y ^{2}}

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\frac{d}{d x} ((x - 1)^{2} (x - 2) (x - 4))

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integral of (6-72x)/(sqrt(1-36x^2))

\int \frac{6 - 72 x}{1 - 36 x ^{2}} d x

derivative of (sqrt(x)/(x+2))

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

Frequently Asked Questions (FAQ)

What is the derivative of 12x^{1/3} ?
The derivative of 12x^{1/3} is 4/(x^{2/3)}
What is the first derivative of 12x^{1/3} ?
The first derivative of 12x^{1/3} is 4/(x^{2/3)}