What is (\partial)/(\partial x)(x^{0.5}+y^{0.5}) ?

The answer to (\partial)/(\partial x)(x^{0.5}+y^{0.5}) is (0.5)/(x^{1/2)}

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(\partial)/(\partial x)(x^{0.5}+y^{0.5})

\frac{\partial}{\partial x} (x^{0.5} + y^{0.5})

\frac{0.5}{x ^{\frac{1}{2}}}

Solution steps

\frac{\partial}{\partial x} (x^{0.5} + y^{0.5})

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (x^{0.5}) + \frac{\partial}{\partial x} (y^{0.5})

\frac{\partial}{\partial x} (x^{0.5}) = \frac{0.5}{x ^{0.5}}

\frac{\partial}{\partial x} (y^{0.5}) = 0

= \frac{0.5}{x ^{0.5}} + 0

Simplify

= \frac{0.5}{x ^{\frac{1}{2}}}

What is (\partial)/(\partial x)(x^{0.5}+y^{0.5}) ?
The answer to (\partial)/(\partial x)(x^{0.5}+y^{0.5}) is (0.5)/(x^{1/2)}