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

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

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

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

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

Solution steps

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

Treat

y

as a constant

Apply the chain rule:

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

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

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

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

Simplify

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

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

\int 5 + \frac{3 x ^{2}}{2 x ^{3} + 7} d x

\int 300 t e^{\frac{- t ^{2}}{7}} d t

x \to 0 lim (\frac{cos ( 5 x )}{x})

\frac{\partial}{\partial x} (6 x^{2} + y^{2} - 7 y)

e^{- 6 s}

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