What is (\partial)/(\partial y)(e^{xy}+2x-5y) ?

The answer to (\partial)/(\partial y)(e^{xy}+2x-5y) is e^{xy}x-5

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(\partial)/(\partial y)(e^{xy}+2x-5y)

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

e^{x y} x - 5

Solution steps

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

Treat

x

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial y} (e^{x y}) + \frac{\partial}{\partial y} (2 x) - \frac{\partial}{\partial y} (5 y)

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

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

\frac{\partial}{\partial y} (5 y) = 5

= e^{x y} x + 0 - 5

Simplify

= e^{x y} x - 5

y = 2 x^{3} - 5 x + 1, (1, - 2)

\int x 1 - x^{2} d x

\int \frac{x + 2}{x ^{2} + 25} d x

f (x) = \frac{10 x}{1 + x ^{2}}, (3, 3)

x^{5} + y^{4} x^{6} + 5 y^{^{'}} = 0

What is (\partial)/(\partial y)(e^{xy}+2x-5y) ?
The answer to (\partial)/(\partial y)(e^{xy}+2x-5y) is e^{xy}x-5