What is (\partial)/(\partial x)(e^{-4x}cos(5x)) ?

The answer to (\partial)/(\partial x)(e^{-4x}cos(5x)) is -4e^{-4x}cos(5x)-5e^{-4x}sin(5x)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

(\partial)/(\partial x)(e^{-4x}cos(5x))

\frac{\partial}{\partial x} (e^{- 4 x} cos (5 x))

- 4 e^{- 4 x} cos (5 x) - 5 e^{- 4 x} sin (5 x)

Solution steps

\frac{\partial}{\partial x} (e^{- 4 x} cos (5 x))

Apply the Product Rule:

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

f = e^{- 4 x}, g = cos (5 x)

= \frac{\partial}{\partial x} (e^{- 4 x}) cos (5 x) + \frac{\partial}{\partial x} (cos (5 x)) e^{- 4 x}

\frac{\partial}{\partial x} (e^{- 4 x}) = - 4 e^{- 4 x}

\frac{\partial}{\partial x} (cos (5 x)) = - sin (5 x) \cdot 5

= (- 4 e^{- 4 x}) cos (5 x) + (- sin (5 x) \cdot 5) e^{- 4 x}

Simplify

= - 4 e^{- 4 x} cos (5 x) - 5 e^{- 4 x} sin (5 x)

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

\frac{d}{d x} (t e^{2 x})

\frac{d ^{2}}{d x ^{2}} (\frac{1}{x})

y = x, 0, 1

\int \frac{8 x ^{7}}{x ^{8} - 1} d x

What is (\partial)/(\partial x)(e^{-4x}cos(5x)) ?
The answer to (\partial)/(\partial x)(e^{-4x}cos(5x)) is -4e^{-4x}cos(5x)-5e^{-4x}sin(5x)