What is (\partial)/(\partial x)(xe^{7xy}) ?

The answer to (\partial)/(\partial x)(xe^{7xy}) is e^{7xy}+7e^{7xy}xy

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(\partial)/(\partial x)(xe^{7xy})

\frac{\partial}{\partial x} (x e^{7 x y})

e^{7 x y} + 7 e^{7 x y} x y

Solution steps

\frac{\partial}{\partial x} (x e^{7 x y})

Treat

y

as a constant

Apply the Product Rule:

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

f = x, g = e^{7 x y}

= \frac{\partial}{\partial x} (x) e^{7 x y} + \frac{\partial}{\partial x} (e^{7 x y}) x

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

\frac{\partial}{\partial x} (e^{7 x y}) = e^{7 x y} \cdot 7 y

= 1 \cdot e^{7 x y} + e^{7 x y} \cdot 7 y x

Simplify

= e^{7 x y} + 7 e^{7 x y} x y

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What is (\partial)/(\partial x)(xe^{7xy}) ?
The answer to (\partial)/(\partial x)(xe^{7xy}) is e^{7xy}+7e^{7xy}xy