What is (\partial)/(\partial x)(7xe^{xy}) ?

The answer to (\partial)/(\partial x)(7xe^{xy}) is 7(e^{xy}+e^{xy}xy)

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(\partial)/(\partial x)(7xe^{xy})

\frac{\partial}{\partial x} (7 x e^{x y})

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

Solution steps

\frac{\partial}{\partial x} (7 x e^{x y})

Treat

y

as a constant

Take the constant out:

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

= 7 \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}

= 7 (\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

= 7 (1 \cdot e^{x y} + e^{x y} y x)

Simplify

= 7 (e^{x y} + e^{x y} x y)

\int \frac{7 + x}{7 - x} d x

\int (1 - cos^{2} (x))^{3} d x

(e^{3 x} - 1)^{5}

\frac{\partial}{\partial x} (- \frac{2 x}{( x + y ) ^{2}})

\frac{d}{d x} (- 3 cos^{12} (x))

What is (\partial)/(\partial x)(7xe^{xy}) ?
The answer to (\partial)/(\partial x)(7xe^{xy}) is 7(e^{xy}+e^{xy}xy)