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

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

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

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

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

Solution steps

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

Treat

y

as a constant

Take the constant out:

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

= - \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}

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

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

Simplify

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

\int_{- 1}^{5} (3 e^{- x})^{2} d x

x \to 1 - lim (x^{(\frac{1}{1 - x})})

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

f (x) = ln (x + 9)

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