What is (\partial)/(\partial x)(e^{xy}+5x-7y+3) ?

The answer to (\partial)/(\partial x)(e^{xy}+5x-7y+3) is e^{xy}y+5

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(\partial)/(\partial x)(e^{xy}+5x-7y+3)

\frac{\partial}{\partial x} (e^{x y} + 5 x - 7 y + 3)

e^{x y} y + 5

Solution steps

\frac{\partial}{\partial x} (e^{x y} + 5 x - 7 y + 3)

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (e^{x y}) + \frac{\partial}{\partial x} (5 x) - \frac{\partial}{\partial x} (7 y) + \frac{\partial}{\partial x} (3)

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

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

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

\frac{\partial}{\partial x} (3) = 0

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

Simplify

= e^{x y} y + 5

x \to 0 - lim (\frac{- 3 x ^{3} + 4 x}{x})

y^{^{''}} + 2 y^{^{'}} - 8 y = 6 e^{- 2 x} - e^{- x}

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

sin (x - 5)

n = 1 \sum \infty \frac{3}{n ln ( 9 n )}

What is (\partial)/(\partial x)(e^{xy}+5x-7y+3) ?
The answer to (\partial)/(\partial x)(e^{xy}+5x-7y+3) is e^{xy}y+5