What is (\partial)/(\partial x)(ysqrt(x)-y^2-x+3y) ?

The answer to (\partial)/(\partial x)(ysqrt(x)-y^2-x+3y) is y/(2sqrt(x))-1

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(\partial)/(\partial x)(ysqrt(x)-y^2-x+3y)

\frac{\partial}{\partial x} (y x - y^{2} - x + 3 y)

\frac{y}{2 x} - 1

Solution steps

\frac{\partial}{\partial x} (y x - y^{2} - x + 3 y)

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (y x) - \frac{\partial}{\partial x} (y^{2}) - \frac{\partial}{\partial x} (x) + \frac{\partial}{\partial x} (3 y)

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

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

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

\frac{\partial}{\partial x} (3 y) = 0

= \frac{y}{2 x} - 0 - 1 + 0

Simplify

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

What is (\partial)/(\partial x)(ysqrt(x)-y^2-x+3y) ?
The answer to (\partial)/(\partial x)(ysqrt(x)-y^2-x+3y) is y/(2sqrt(x))-1