What is the derivative of-3/4 x^{1/3} ?

The derivative of-3/4 x^{1/3} is -1/(4x^{2/3)}

What is the first derivative of-3/4 x^{1/3} ?

The first derivative of-3/4 x^{1/3} is -1/(4x^{2/3)}

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\frac{d}{d x} (- \frac{3}{4} x^{\frac{1}{3}})

- \frac{1}{4 x ^{\frac{2}{3}}}

Solution steps

\frac{d}{d x} (- \frac{3}{4} x^{\frac{1}{3}})

Simplify

- \frac{3}{4} x^{\frac{1}{3}} : - \frac{3 x ^{\frac{1}{3}}}{4}

= \frac{d}{d x} (- \frac{3 x ^{\frac{1}{3}}}{4})

Take the constant out:

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

= - \frac{3}{4} \frac{d}{d x} (x^{\frac{1}{3}})

Apply the Power Rule:

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

= - \frac{3}{4} \cdot \frac{1}{3} x^{\frac{1}{3} - 1}

Simplify

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

= - \frac{1}{4 x ^{\frac{2}{3}}}

y^{^{'}} - \frac{3 y}{x} = x

sin (x^{2}) + \frac{( 1 - x )}{1 + x}

\frac{\partial}{\partial x} (\frac{2}{x + 2 y})

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

\frac{d}{d x} (- 1 - 4 sin (x))

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