What is (\partial)/(\partial y)(2e^{2z}xy-2y) ?

The answer to (\partial)/(\partial y)(2e^{2z}xy-2y) is 2xe^{2z}-2

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(\partial)/(\partial y)(2e^{2z}xy-2y)

\frac{\partial}{\partial y} (2 e^{2 z} x y - 2 y)

2 x e^{2 z} - 2

Solution steps

\frac{\partial}{\partial y} (2 e^{2 z} x y - 2 y)

Treat

z, x

as constants

Apply the Sum/Difference Rule:

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

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

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

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

= 2 x e^{2 z} - 2

\frac{1}{x ^{3}}

\frac{d}{d t} (cos (t) - sin (t))

\int + \frac{e ^{2 x}}{1 + e ^{2 x}} d x

f (x) = 4 x^{2} - 4 x + 1, at x = 1

\frac{\partial}{\partial x} (x sin (x + y) - cos (x + y))

What is (\partial)/(\partial y)(2e^{2z}xy-2y) ?
The answer to (\partial)/(\partial y)(2e^{2z}xy-2y) is 2xe^{2z}-2