What is (\partial)/(\partial x)(xe^{xy+1}) ?

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

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(\partial)/(\partial x)(xe^{xy+1})

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

e^{x y + 1} + e^{x y + 1} x y

Solution steps

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

Treat

y

as a constant

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x, g = e^{x y + 1}

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

\frac{\partial}{\partial x} (x) = 1

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

= 1 \cdot e^{x y + 1} + e^{x y + 1} y x

Simplify

= e^{x y + 1} + e^{x y + 1} x y

\frac{\partial}{\partial y} (2 x sin (x^{2} y))

\frac{d}{d x} (5 x^{2} + 3 x - 2)

(- 8, - 14), (61, - 32)

- \frac{d y}{d x} = 4 x^{3} y

h \to 0 lim (\frac{1}{2 ^{h}})

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