What is (\partial)/(\partial x)(3(x^{1/3}+y^{1/3})) ?

The answer to (\partial)/(\partial x)(3(x^{1/3}+y^{1/3})) is 1/(x^{2/3)}

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(\partial)/(\partial x)(3(x^{1/3}+y^{1/3}))

\frac{\partial}{\partial x} (3 (x^{\frac{1}{3}} + y^{\frac{1}{3}}))

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

Solution steps

\frac{\partial}{\partial x} (3 (x^{\frac{1}{3}} + y^{\frac{1}{3}}))

Treat

y

as a constant

Take the constant out:

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

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

Apply the Sum/Difference Rule:

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

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

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

\frac{\partial}{\partial x} (y^{\frac{1}{3}}) = 0

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

Simplify

3 (\frac{1}{3 x ^{\frac{2}{3}}} + 0) : \frac{1}{x ^{\frac{2}{3}}}

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

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What is (\partial)/(\partial x)(3(x^{1/3}+y^{1/3})) ?
The answer to (\partial)/(\partial x)(3(x^{1/3}+y^{1/3})) is 1/(x^{2/3)}