What is (\partial)/(\partial x)(x+sqrt(x)sqrt(y)) ?

The answer to (\partial)/(\partial x)(x+sqrt(x)sqrt(y)) is 1+(sqrt(y))/(2sqrt(x))

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(\partial)/(\partial x)(x+sqrt(x)sqrt(y))

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

1 + \frac{y}{2 x}

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

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

\frac{\partial}{\partial x} (x y) = \frac{y}{2 x}

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

\frac{d}{d x} (\frac{2 x ^{\frac{3}{2}} - x ^{2} + 4}{x})

\frac{d}{d x} (\frac{1}{x ^{7}} + \frac{2}{x ^{3}})

\int_{- 1}^{1} 2 - 2 x^{2} d x

y^{^{''}} + 2 y^{^{'}} + y = x^{2} e^{- x}

tan (t)

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