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

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

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(\partial)/(\partial y)(y/(2sqrt(x))-1)

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

\frac{1}{2 x}

Solution steps

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

Treat

x

as a constant

Apply the Sum/Difference Rule:

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

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

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

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

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

Simplify

= \frac{1}{2 x}

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

\frac{\partial}{\partial x} (x^{7} + x y^{9} + 1)

\frac{d}{d x} (27 arctan (x))

\frac{\partial}{\partial x} (x^{2} + x y + 3 x + 2 y + 5)

y^{^{''}} + 4 y^{^{'}} + 4 y = - 3 e^{2 t}, y (0) = 1, y^{^{'}} (0) = 0

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