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

The answer to (\partial)/(\partial x)(e^y+xe^{xy}) is e^{yx}+e^{yx}yx

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(\partial)/(\partial x)(e^y+xe^{xy})

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

e^{y x} + e^{y x} y x

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

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

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

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

Simplify

= e^{y x} + e^{y x} y x

x^{3} f (x)

\int_{3}^{6} 4 d x

\frac{\partial}{\partial x} ((x + 2)^{2} - 2 (y - 1)^{2} - 5)

sin (x) + cos (x)

y^{^{''}} + 4 y^{^{'}} + 3 y = x

What is (\partial)/(\partial x)(e^y+xe^{xy}) ?
The answer to (\partial)/(\partial x)(e^y+xe^{xy}) is e^{yx}+e^{yx}yx