What is (\partial)/(\partial y)(2xe^{-2xy}) ?

The answer to (\partial)/(\partial y)(2xe^{-2xy}) is -4e^{-2xy}x^2

Popular >

(\partial)/(\partial y)(2xe^{-2xy})

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

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

Solution steps

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

Treat

x

as a constant

Take the constant out:

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

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

Apply the chain rule:

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

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

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

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

Simplify

2 x e^{- 2 x y} (- 2 x) : - 4 e^{- 2 x y} x^{2}

= - 4 e^{- 2 x y} x^{2}

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

x + x + x

y^{^{''}} + 6 y^{^{'}} + 5 y = 12 t e^{5 t}

x \to 2 lim (4 x^{2} + 3)

x \to 1 lim (2 x^{2} + 1)

What is (\partial)/(\partial y)(2xe^{-2xy}) ?
The answer to (\partial)/(\partial y)(2xe^{-2xy}) is -4e^{-2xy}x^2