What is (\partial)/(\partial y)(1+e^xy+xe^xy) ?

The answer to (\partial)/(\partial y)(1+e^xy+xe^xy) is e^xx+e^x

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(\partial)/(\partial y)(1+e^xy+xe^xy)

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

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

Solution steps

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

Treat

x

as a constant

Apply the Sum/Difference Rule:

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

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

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

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

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

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

Simplify

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

y^{^{''}} - 6 y^{^{'}} + 9 y = t^{- 4} e^{3 t}

f (x) = (2 x - 8)^{5}

2 x^{3} + 4 x^{2} - 5 x - 3

\frac{d}{d x} (2 sin (5 x))

x \to 0 + lim (8 x ln (x))

What is (\partial)/(\partial y)(1+e^xy+xe^xy) ?
The answer to (\partial)/(\partial y)(1+e^xy+xe^xy) is e^xx+e^x