What is (\partial)/(\partial x)(ysqrt(x)-y^2-2x+7y) ?

The answer to (\partial)/(\partial x)(ysqrt(x)-y^2-2x+7y) is y/(2sqrt(x))-2

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(\partial)/(\partial x)(ysqrt(x)-y^2-2x+7y)

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

\frac{y}{2 x} - 2

Solution steps

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

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

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

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

\frac{\partial}{\partial x} (7 y) = 0

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

Simplify

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

cos (x) + sin (x)

\frac{\partial}{\partial x} (- 2 y cos (x))

tan (9 x)

\int e^{2 x} sin (2 x) d x

\frac{d}{d x} y + y x^{7} = 0

What is (\partial)/(\partial x)(ysqrt(x)-y^2-2x+7y) ?
The answer to (\partial)/(\partial x)(ysqrt(x)-y^2-2x+7y) is y/(2sqrt(x))-2