What is (\partial)/(\partial y)(3xe^{-2xy}) ?

The answer to (\partial)/(\partial y)(3xe^{-2xy}) is -6e^{-2xy}x^2

Popular >

(\partial)/(\partial y)(3xe^{-2xy})

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

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

Solution steps

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

Treat

x

as a constant

Take the constant out:

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

= 3 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

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

Simplify

3 x e^{- 2 x y} (- 2 x) : - 6 e^{- 2 x y} x^{2}

= - 6 e^{- 2 x y} x^{2}

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

\int \frac{1}{x ^{2} + 4 x + 8} d x

\frac{d}{d x} ((3 x - 5)^{4})

5 e^{2 x} \frac{d y}{d x} = - 10 \frac{x}{y ^{2}}

f (x) = \frac{1}{2 x}, at x = 49

What is (\partial)/(\partial y)(3xe^{-2xy}) ?
The answer to (\partial)/(\partial y)(3xe^{-2xy}) is -6e^{-2xy}x^2