What is (\partial)/(\partial x)(y^2e^{x+3y}) ?

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

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(\partial)/(\partial x)(y^2e^{x+3y})

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

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

Solution steps

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

Treat

y

as a constant

Take the constant out:

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

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

Apply the chain rule:

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

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

\frac{\partial}{\partial x} (x + 3 y) = 1

= y^{2} e^{x + 3 y} \cdot 1

Simplify

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

\int (e^{2 x} cos (e^{x})) d x

\int sin (3 x) e^{- 2 x} d x

\int_{0}^{10} (2200 e^{0.024 t} - 1460 e^{0.018 t}) d t

\int x^{2} - 9 d x

\frac{d y}{d x} + 3 y = - y^{2}

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