What is (\partial)/(\partial x)(3xye^{y-x}) ?

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

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(\partial)/(\partial x)(3xye^{y-x})

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

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

Solution steps

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

Treat

y

as a constant

Take the constant out:

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

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

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

(3, 3), (2, - 5)

(x^{2} - 5) y y^{^{'}} = 2 x

\int \frac{x}{3} \cdot sin (x^{2}) d x

\int (x) d x

12 x^{2} - 8 x - 4

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