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

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

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(\partial)/(\partial x)(x^{1/2}+y^{1/3})

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

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

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

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

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

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

Simplify

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

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