What is (\partial)/(\partial x)(1+x^2y-sqrt(xy)) ?

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

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(\partial)/(\partial x)(1+x^2y-sqrt(xy))

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

2 x y - \frac{y}{2 x}

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

\frac{\partial}{\partial x} (1) = 0

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

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

= 0 + 2 y x - \frac{y}{2 x}

Simplify

= 2 x y - \frac{y}{2 x}

\frac{d}{d t} (2 t + 2)

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

\frac{4 s}{s ^{2} - 16}

\frac{d}{d x} (sin (x + \frac{π}{2}) - cos (x))

1 - 3 x^{2}

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