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

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

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(\partial)/(\partial x)(6xe^{x+y})

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

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

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}

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

Simplify

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

x \to 3 - lim (2 3 - x)

\frac{d}{d y} (- y^{2})

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\int \frac{x ^{4} + 9}{x ^{3}} d x

x y^{^{'}} = - 3 y

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