What is (\partial)/(\partial x)(6xe^{xy}) ?

The answer to (\partial)/(\partial x)(6xe^{xy}) is 6(e^{xy}+e^{xy}xy)

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(\partial)/(\partial x)(6xe^{xy})

\frac{\partial}{\partial x} (6 x e^{x y})

6 (e^{x y} + e^{x y} x y)

Solution steps

\frac{\partial}{\partial x} (6 x e^{x y})

Treat

y

as a constant

Take the constant out:

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

= 6 \frac{\partial}{\partial x} (x e^{x y})

Apply the Product Rule:

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

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

= 6 (\frac{\partial}{\partial x} (x) e^{x y} + \frac{\partial}{\partial x} (e^{x y}) x)

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

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

= 6 (1 \cdot e^{x y} + e^{x y} y x)

Simplify

= 6 (e^{x y} + e^{x y} x y)

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\frac{d}{d x} (2 (13 - x^{4}))

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\frac{d}{d x} ((6 x + 5) (x^{3} - 2))

What is (\partial)/(\partial x)(6xe^{xy}) ?
The answer to (\partial)/(\partial x)(6xe^{xy}) is 6(e^{xy}+e^{xy}xy)