What is the derivative of (6x/(2x^{1/3)}) ?

The derivative of (6x/(2x^{1/3)}) is 2/(x^{1/3)}

What is the first derivative of (6x/(2x^{1/3)}) ?

The first derivative of (6x/(2x^{1/3)}) is 2/(x^{1/3)}

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\frac{d}{d x} (\frac{6 x}{2 x ^{\frac{1}{3}}})

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

Solution steps

\frac{d}{d x} (\frac{6 x}{2 x ^{\frac{1}{3}}})

Simplify

\frac{6 x}{2 x ^{\frac{1}{3}}} : 3 x^{\frac{2}{3}}

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

Take the constant out:

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

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

Apply the Power Rule:

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

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

Simplify

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

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

y^{^{''}} + y = sin (x)

\int_{0}^{1} 40 \frac{1}{x ^{p}} d x

\int \frac{( ( ( x ) + 1 ) \cdot ( x - 1 ) )}{( x )} d x

f (x) = x^{2} + 2, (- 2, 6)

What is the derivative of (6x/(2x^{1/3)}) ?
The derivative of (6x/(2x^{1/3)}) is 2/(x^{1/3)}
What is the first derivative of (6x/(2x^{1/3)}) ?
The first derivative of (6x/(2x^{1/3)}) is 2/(x^{1/3)}