What is (\partial)/(\partial y)(3xe^{9xy}) ?

The answer to (\partial)/(\partial y)(3xe^{9xy}) is 27e^{9xy}x^2

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(\partial)/(\partial y)(3xe^{9xy})

\frac{\partial}{\partial y} (3 x e^{9 x y})

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

Solution steps

\frac{\partial}{\partial y} (3 x e^{9 x y})

Treat

x

as a constant

Take the constant out:

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

= 3 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

= 3 x e^{9 x y} \cdot 9 x

Simplify

3 x e^{9 x y} \cdot 9 x : 27 e^{9 x y} x^{2}

= 27 e^{9 x y} x^{2}

\int \frac{tan ( x )}{sec ( x ) tan ( x )} d x

\int_{1}^{5} (2 x - 1)^{\frac{5}{2}} d x

\int 15 x e^{x^{2}} d x

\frac{d}{d x} (ln (\frac{2 x}{x + 9}))

x \to 0 - lim (x + 1)

What is (\partial)/(\partial y)(3xe^{9xy}) ?
The answer to (\partial)/(\partial y)(3xe^{9xy}) is 27e^{9xy}x^2