What is (\partial)/(\partial x)(x^2e^{7xy}) ?

The answer to (\partial)/(\partial x)(x^2e^{7xy}) is 2xe^{7xy}+e^{7xy}*7yx^2

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(\partial)/(\partial x)(x^2e^{7xy})

\frac{\partial}{\partial x} (x^{2} e^{7 x y})

2 x e^{7 x y} + e^{7 x y} \cdot 7 y x^{2}

Solution steps

\frac{\partial}{\partial x} (x^{2} e^{7 x y})

Treat

y

as a constant

Apply the Product Rule:

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

f = x^{2}, g = e^{7 x y}

= \frac{\partial}{\partial x} (x^{2}) e^{7 x y} + \frac{\partial}{\partial x} (e^{7 x y}) x^{2}

\frac{\partial}{\partial x} (x^{2}) = 2 x

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

= 2 x e^{7 x y} + e^{7 x y} \cdot 7 y x^{2}

\int 2 x (x^{2} + 2)^{9} d x

\frac{\partial ^{2}}{\partial u ( v ) \partial v} (e^{u (v) v})

\frac{d}{d x} ((a x + b) e^{2 x})

\int \frac{x + 4}{x ^{2} + 9} d x

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

What is (\partial)/(\partial x)(x^2e^{7xy}) ?
The answer to (\partial)/(\partial x)(x^2e^{7xy}) is 2xe^{7xy}+e^{7xy}*7yx^2