What is (\partial)/(\partial x)(5xye^{(x+y)}) ?

The answer to (\partial)/(\partial x)(5xye^{(x+y)}) is 5y(e^{x+y}+e^{x+y}x)

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(\partial)/(\partial x)(5xye^{(x+y)})

\frac{\partial}{\partial x} (5 x y e^{(x + y)})

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

Solution steps

\frac{\partial}{\partial x} (5 x y e^{(x + y)})

Treat

y

as a constant

Take the constant out:

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

= 5 y \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}

= 5 y (\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}

= 5 y (1 \cdot e^{x + y} + e^{x + y} x)

Simplify

= 5 y (e^{x + y} + e^{x + y} x)

\frac{d}{d x} (2 x + \frac{4 x}{3 x - 1})

f (x) = \frac{4 x}{x ^{2} - 5}, at x = 3

\int \frac{1}{x x ^{2} - 9} d x

\int_{0}^{2} 1

\int (3 x^{5} - 4)^{2} \cdot 5 x^{4} d x

What is (\partial)/(\partial x)(5xye^{(x+y)}) ?
The answer to (\partial)/(\partial x)(5xye^{(x+y)}) is 5y(e^{x+y}+e^{x+y}x)