What is (\partial)/(\partial x)(3e^{xy}) ?

The answer to (\partial)/(\partial x)(3e^{xy}) is 3e^{xy}y

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(\partial)/(\partial x)(3e^{xy})

\frac{\partial}{\partial x} (3 e^{x y})

3 e^{x y} y

Solution steps

\frac{\partial}{\partial x} (3 e^{x y})

Treat

y

as a constant

Take the constant out:

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

= 3 \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

= 3 e^{x y} y

- ln (1 - x)

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

\int_{0}^{1} \frac{1}{3 - 2 x} d x

f (x) = x^{2}, at x = 4

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

What is (\partial)/(\partial x)(3e^{xy}) ?
The answer to (\partial)/(\partial x)(3e^{xy}) is 3e^{xy}y