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

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

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

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

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

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

\frac{\partial}{\partial x} (y^{\frac{1}{2}}) = 0

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

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

Simplify

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

f (x) = 8 x^{2} + 5 x, at 53

e^{20 t + 20}

\frac{\partial}{\partial y} (∣ x ∣ y + 2 x)

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

\frac{d}{d x} (- 8 sin (x))

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