What is (\partial)/(\partial y)(ysqrt(x)-y^2-x+6y) ?

The answer to (\partial)/(\partial y)(ysqrt(x)-y^2-x+6y) is sqrt(x)+6-2y

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(\partial)/(\partial y)(ysqrt(x)-y^2-x+6y)

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

x + 6 - 2 y

Solution steps

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

Treat

x

as a constant

Apply the Sum/Difference Rule:

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

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

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

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

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

\frac{\partial}{\partial y} (6 y) = 6

= x - 2 y - 0 + 6

Simplify

= x + 6 - 2 y

\int x^{5} (3 x^{2} + 4) d x

\frac{d}{d x} (ln (tan (x^{2})))

\frac{d}{d x} (arctan (x) + x - 1)

y^{^{''}} - 16 y^{^{'}} + 73 = 0, y (0) = 6, y^{^{'}} (0) = 6

\frac{d}{d x} (\frac{1}{2} (4 x^{2} + x)^{- 3})

What is (\partial)/(\partial y)(ysqrt(x)-y^2-x+6y) ?
The answer to (\partial)/(\partial y)(ysqrt(x)-y^2-x+6y) is sqrt(x)+6-2y