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

The answer to (\partial)/(\partial x)(xe^{xy}-x/(y^2)) is e^{yx}+ye^{yx}x-1/(y^2)

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(\partial)/(\partial x)(xe^{xy}-x/(y^2))

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

e^{y x} + y e^{y x} x - \frac{1}{y ^{2}}

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

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

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

= e^{y x} + y e^{y x} x - \frac{1}{y ^{2}}

\frac{( 8 e ^{(9 x)} )}{( 5 x - 2 )}

\frac{d}{d x} (x e^{7 x})

\int (2 x + 1) d x

\frac{d}{d x} (3 x^{2} sin (4 x))

\frac{d}{d x} (x^{- 2 c o s (x)})

What is (\partial)/(\partial x)(xe^{xy}-x/(y^2)) ?
The answer to (\partial)/(\partial x)(xe^{xy}-x/(y^2)) is e^{yx}+ye^{yx}x-1/(y^2)