What is (\partial)/(\partial y)(xe^{2x-3y}) ?

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

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(\partial)/(\partial y)(xe^{2x-3y})

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

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

Solution steps

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

Treat

x

as a constant

Take the constant out:

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

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

Apply the chain rule:

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

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

\frac{\partial}{\partial y} (2 x - 3 y) = - 3

= x e^{2 x - 3 y} (- 3)

Simplify

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

x \to 0 lim (\frac{sin ( 4 x ) cos ( 3 x )}{7 x})

x \to 0 lim (x^{x^{3}})

x \to 1 lim (3 x - 4)

e^{x^{4} + 9 x}

\frac{d y}{d x}, 5 cos (x y) = 6 x + 7 y

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