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

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

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

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

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

Solution steps

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

Treat

y

as a constant

Take the constant out:

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

= 3 \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}

= 3 (\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

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

Simplify

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

x \to - \infty lim (0^{x})

x \to 0 + lim (ln (5) sin (x))

\int_{4}^{16} \frac{1}{6 - x} d x

\frac{d y}{d x}, x y = 8

\int - \frac{e ^{- s t}}{s} d t

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