What is (\partial)/(\partial x)(e^{(4xy)}) ?

The answer to (\partial)/(\partial x)(e^{(4xy)}) is e^{4xy}*4y

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(\partial)/(\partial x)(e^{(4xy)})

\frac{\partial}{\partial x} (e^{(4 x y)})

e^{4 x y} \cdot 4 y

Solution steps

\frac{\partial}{\partial x} (e^{(4 x y)})

Treat

y

as a constant

Apply the chain rule:

e^{4 x y} \frac{\partial}{\partial x} (4 x y)

= e^{4 x y} \frac{\partial}{\partial x} (4 x y)

\frac{\partial}{\partial x} (4 x y) = 4 y

= e^{4 x y} \cdot 4 y

What is (\partial)/(\partial x)(e^{(4xy)}) ?
The answer to (\partial)/(\partial x)(e^{(4xy)}) is e^{4xy}*4y