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

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

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

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

7 e^{7 x y} x^{2}

Solution steps

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

Treat

x

as a constant

Take the constant out:

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

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

Apply the chain rule:

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

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

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

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

Simplify

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

= 7 e^{7 x y} x^{2}

\int e^{(x - 1)} d x

\frac{d y}{d x} = y e^{- x^{2}}

\frac{\partial}{\partial x} (e^{x + y + 9})

\int e^{\frac{r}{2}} d r

\int - 10 d x

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