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)}

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

\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}}}

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

(4 π r^{2})^{^{'}}

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

y = \frac{2 x}{( x ^{2} + 1 )}

\int \frac{8}{( 4 x ^{2} + 1 ) ^{2}} d x

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)}