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

f (x) = \frac{x ^{2}}{2}

d V = 6 d t

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

\int 5 x (x^{2} + 1)^{3} d x

\int_{- 3}^{2} 6 - x - 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