What is (\partial)/(\partial y)(xe^{xy}-2y+1) ?

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

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(\partial)/(\partial y)(xe^{xy}-2y+1)

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

e^{x y} x^{2} - 2

Solution steps

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

Treat

x

as a constant

Apply the Sum/Difference Rule:

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

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

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

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

\frac{\partial}{\partial y} (1) = 0

= x^{2} e^{x y} - 2 + 0

Simplify

= e^{x y} x^{2} - 2

ln (x)

\frac{d}{d x} ((x^{2} + y^{2} + z^{2})^{\frac{1}{2}})

\frac{d}{d x} (6 ln (sec (x) + tan (x)))

cos^{3} (x)

\frac{1}{s ^{2} ( s ^{2} + 9 )}

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