What is (\partial)/(\partial y)((x+y)*e^{x+2y}) ?

The answer to (\partial)/(\partial y)((x+y)*e^{x+2y}) is e^{x+2y}+2e^{x+2y}(x+y)

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(\partial)/(\partial y)((x+y)*e^{x+2y})

\frac{\partial}{\partial y} ((x + y) \cdot e^{x + 2 y})

e^{x + 2 y} + 2 e^{x + 2 y} (x + y)

Solution steps

\frac{\partial}{\partial y} ((x + y) e^{x + 2 y})

Treat

x

as a constant

Apply the Product Rule:

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

f = x + y, g = e^{x + 2 y}

= \frac{\partial}{\partial y} (x + y) e^{x + 2 y} + \frac{\partial}{\partial y} (e^{x + 2 y}) (x + y)

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

\frac{\partial}{\partial y} (e^{x + 2 y}) = e^{x + 2 y} \cdot 2

= 1 \cdot e^{x + 2 y} + e^{x + 2 y} \cdot 2 (x + y)

Simplify

= e^{x + 2 y} + 2 e^{x + 2 y} (x + y)

\frac{2 x ^{2} - 3 x + 1}{x}

p

\frac{\partial}{\partial x} (2 x y + y^{2})

(- 4.5) (1.1)

1 - sec (x)

What is (\partial)/(\partial y)((x+y)*e^{x+2y}) ?
The answer to (\partial)/(\partial y)((x+y)*e^{x+2y}) is e^{x+2y}+2e^{x+2y}(x+y)