What is (\partial)/(\partial y)((xe^y)^2) ?

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

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(\partial)/(\partial y)((xe^y)^2)

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

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

Solution steps

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

Simplify

(x e^{y})^{2} : e^{2 y} x^{2}

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

Treat

x

as a constant

Take the constant out:

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

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

Apply the chain rule:

e^{2 y} \frac{\partial}{\partial y} (2 y)

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

\frac{\partial}{\partial y} (2 y) = 2

= x^{2} e^{2 y} \cdot 2

x \to - \infty lim (\frac{7}{x})

d er i v a t i v e (ln (5 x))^{2}

\int x - \frac{2}{x} d x

\frac{\partial}{\partial x} (5 x^{2})

\int \frac{x}{6 - x ^{2}} d x

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