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

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

Popular >

(\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}) = e^{x y} y

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

Simplify

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

x sin (y)

x \to - \infty lim (- 2 x - 1)

\int 25 - 4 x^{2} d x

y = 2 sin (x), at x = \frac{π}{4}

\int sec^{3} (x) tan^{2} (x) d x

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