What is the d/(dy)((x)2xe^{-xy}) ?

The d/(dy)((x)2xe^{-xy}) is -2e^{-xy}x^3

What is the first d/(dy)((x)2xe^{-xy}) ?

The first d/(dy)((x)2xe^{-xy}) is -2e^{-xy}x^3

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

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

Solution steps

\frac{d}{d y} ((x) \cdot 2 x e^{- x y})

Simplify

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

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

Treat

x

as a constant

Take the constant out:

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

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

Apply the chain rule:

e^{- x y} \frac{d}{d y} (- x y)

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

\frac{d}{d y} (- x y) = - x

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

Simplify

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

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

e^{- a} e^{- b} e^{- c}

(41)^{\frac{3}{2}}

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

6.022 \cdot (1 0^{2})^{3} \cdot 2

What is the d/(dy)((x)2xe^{-xy}) ?
The d/(dy)((x)2xe^{-xy}) is -2e^{-xy}x^3
What is the first d/(dy)((x)2xe^{-xy}) ?
The first d/(dy)((x)2xe^{-xy}) is -2e^{-xy}x^3