What is (\partial)/(\partial x)(2e^{xy}) ?

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

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(\partial)/(\partial x)(2e^{xy})

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

2 e^{x y} y

Solution steps

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

Treat

y

as a constant

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the chain rule:

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

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

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

= 2 e^{x y} y

\int \frac{2 - x ^{2}}{x} d x

x e^{x}, 0

\int - \frac{2}{3} x cos (3 x) d x

f (t) = t e^{t} cot (t)

f (x) = \frac{5}{x}, x = - 1

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