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

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

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

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

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

Solution steps

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

Treat

y

as a constant

Take the constant out:

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

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

Apply the Product Rule:

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

f = x, g = e^{- 3 x y}

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

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

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

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

Simplify

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

\int 2 x (x^{2} + 15)^{7} d x

\frac{d}{d x} (5 + cos (x))

y^{^{'}} + 2 y = x y^{2}

f (x) = (2 x - 8)^{4} (x^{2} + x + 1)^{5}

y = x^{3} - 10 x^{2} + 21 x, y = - x^{3} + 10 x^{2} - 21 x

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