What is (\partial)/(\partial y)(xe^{9xy}) ?

The answer to (\partial)/(\partial y)(xe^{9xy}) is 9e^{9xy}x^2

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(\partial)/(\partial y)(xe^{9xy})

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

9 e^{9 x y} x^{2}

Solution steps

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

Treat

x

as a constant

Take the constant out:

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

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

Apply the chain rule:

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

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

\frac{\partial}{\partial y} (9 x y) = 9 x

= x e^{9 x y} \cdot 9 x

Simplify

x e^{9 x y} \cdot 9 x : 9 e^{9 x y} x^{2}

= 9 e^{9 x y} x^{2}

x + 2, x^{2} - 4

\frac{\partial}{\partial x} (3 y^{2})

\int e^{r} (2 + 3 e^{r})^{\frac{3}{2}} d r

\int cos (w n t) d t

\frac{d}{d x} (y - 5 ln ∣ y ∣ + x y)

What is (\partial)/(\partial y)(xe^{9xy}) ?
The answer to (\partial)/(\partial y)(xe^{9xy}) is 9e^{9xy}x^2