What is (\partial)/(\partial x)(e^{-x}sin(x+y)) ?

The answer to (\partial)/(\partial x)(e^{-x}sin(x+y)) is -e^{-x}sin(x+y)+e^{-x}cos(x+y)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

(\partial)/(\partial x)(e^{-x}sin(x+y))

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

- e^{- x} sin (x + y) + e^{- x} cos (x + y)

Solution steps

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

Treat

y

as a constant

Apply the Product Rule:

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

f = e^{- x}, g = sin (x + y)

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

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

\frac{\partial}{\partial x} (sin (x + y)) = cos (x + y)

= (- e^{- x}) sin (x + y) + cos (x + y) e^{- x}

Simplify

= - e^{- x} sin (x + y) + e^{- x} cos (x + y)

\frac{d}{d x} (0.5 x^{2})

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

(5.5) (0.4)

\frac{2}{( s ^{2} + 4 )}

y = x, y = 2 x 1 - x^{2}

What is (\partial)/(\partial x)(e^{-x}sin(x+y)) ?
The answer to (\partial)/(\partial x)(e^{-x}sin(x+y)) is -e^{-x}sin(x+y)+e^{-x}cos(x+y)