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

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

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

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

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

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

Solution steps

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

Apply the Sum/Difference Rule:

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

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

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

\frac{d}{d x} (3) = 0

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

Simplify

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

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y^{^{'}} + \frac{1}{20 x} y = - 9.81

\frac{d}{d x} (5 - cos (x))

\frac{\partial}{\partial x} (2 (x - 1)^{2} - 3 y - 5)

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