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

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

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

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

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

Solution steps

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

Treat

y

as a constant

Take the constant out:

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

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

Apply the Product Rule:

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

f = x, g = e^{7 x y}

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

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

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

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

Simplify

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

\int \frac{x - 1}{x ^{3} + x ^{2}} d x

(1 - x^{2}) y^{^{'}} + x y = x

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

x \to \infty lim (x^{2} - 4 x)

f (x) = 4 sin^{3} (x)

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