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

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

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

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

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

Solution steps

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

Treat

y

as a constant

Take the constant out:

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

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

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

e^{- 2 s} \frac{1}{10 s + 2}

\frac{d}{d x} (2 x^{\frac{3}{2}} + 7)

\int \frac{( ln ( x ) ) ^{11}}{x} d x

(arctan (x))^{^{'}}

\frac{d}{d x} (8 e^{x} + \frac{8}{3 x})

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