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

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

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

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

- 9 e^{3 x y} x^{2}

Solution steps

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

Treat

x

as a constant

Take the constant out:

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

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

Apply the chain rule:

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

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

\frac{\partial}{\partial y} (3 x y) = 3 x

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

Simplify

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

= - 9 e^{3 x y} x^{2}

x \to 8 lim (1)

\frac{d}{d x} (- π)

\int (sec (5 x) + csc (5 x))^{2} d x

\int \frac{3 x ^{2} + 15 x}{( x - 1 ) ^{2} ( x + 2 )} d x

n = 8 \sum \infty cos (\frac{1}{n ^{3}})

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