What is the derivative of x^{2/3}-x^{1/3}+4 ?

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

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

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

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\frac{d}{d x} (x^{\frac{2}{3}} - x^{\frac{1}{3}} + 4)

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

Solution steps

\frac{d}{d x} (x^{\frac{2}{3}} - x^{\frac{1}{3}} + 4)

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (x^{\frac{2}{3}}) - \frac{d}{d x} (x^{\frac{1}{3}}) + \frac{d}{d x} (4)

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

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

\frac{d}{d x} (4) = 0

= \frac{2}{3 x ^{\frac{1}{3}}} - \frac{1}{3 x ^{\frac{2}{3}}} + 0

Simplify

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

\frac{d}{d y} (- y)

\int x e^{12 x} d x

\frac{\partial}{\partial x} (- 4 x)

\int \frac{1}{2 x - 5} d x

\frac{\partial}{\partial x} (2 zy)

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