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

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

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

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

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

Solution steps

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

Treat

y

as a constant

Take the constant out:

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

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

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x, g = e^{- x^{2} y}

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

\frac{\partial}{\partial x} (x) = 1

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

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

Simplify

3 y (1 \cdot e^{- x^{2} y} + (- 2 y e^{- y x^{2}} x) x) : 3 y (e^{- x^{2} y} - 2 e^{- x^{2} y} x^{2} y)

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

n = 2 \sum \infty \frac{1}{n - 1} - \frac{1}{n}

\frac{d}{d x} (\frac{x ^{2}}{4} + 17)

n \to \infty lim (- 1 + \frac{1}{n})

\int \frac{x ^{2} + 3 x - 1}{x ^{3} + 8} d x

\int x 6 1 + x^{2} d x

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