What is (\partial)/(\partial x)(9xe^{x+y}) ?

The answer to (\partial)/(\partial x)(9xe^{x+y}) is 9(e^{x+y}+e^{x+y}x)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

(\partial)/(\partial x)(9xe^{x+y})

\frac{\partial}{\partial x} (9 x e^{x + y})

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

Solution steps

\frac{\partial}{\partial x} (9 x e^{x + y})

Treat

y

as a constant

Take the constant out:

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

= 9 \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}

= 9 (\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}

= 9 (1 \cdot e^{x + y} + e^{x + y} x)

Simplify

= 9 (e^{x + y} + e^{x + y} x)

y^{^{''}} + 4 y^{^{'}} + 5 y = - 5 x + 5 e^{- x}

\int \frac{3}{2} e^{2 x} d x

x y^{^{'}} + y = y^{2}, y (1) = - 5

(4 e^{2 x})^{^{'}}

(x) \to (0) lim (\frac{1}{2})

What is (\partial)/(\partial x)(9xe^{x+y}) ?
The answer to (\partial)/(\partial x)(9xe^{x+y}) is 9(e^{x+y}+e^{x+y}x)