What is the derivative of-e^{-x}cos(x-e^{-x}sin(x)) ?

The derivative of-e^{-x}cos(x-e^{-x}sin(x)) is 2e^{-x}sin(x)

What is the first derivative of-e^{-x}cos(x-e^{-x}sin(x)) ?

The first derivative of-e^{-x}cos(x-e^{-x}sin(x)) is 2e^{-x}sin(x)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

\frac{d}{d x} (- e^{- x} cos (x) - e^{- x} sin (x))

2 e^{- x} sin (x)

Solution steps

\frac{d}{d x} (- e^{- x} cos (x) - e^{- x} sin (x))

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= - \frac{d}{d x} (e^{- x} cos (x)) - \frac{d}{d x} (e^{- x} sin (x))

\frac{d}{d x} (e^{- x} cos (x)) = - e^{- x} cos (x) - e^{- x} sin (x)

\frac{d}{d x} (e^{- x} sin (x)) = - e^{- x} sin (x) + e^{- x} cos (x)

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

Simplify

- (- e^{- x} cos (x) - e^{- x} sin (x)) - (- e^{- x} sin (x) + e^{- x} cos (x)) : 2 e^{- x} sin (x)

= 2 e^{- x} sin (x)

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

\int e^{1 - 2 t} d t

\int 2 - 3 x d x

\frac{\partial}{\partial x} (4 y^{8} + 3 y^{2} x^{2})

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

What is the derivative of-e^{-x}cos(x-e^{-x}sin(x)) ?
The derivative of-e^{-x}cos(x-e^{-x}sin(x)) is 2e^{-x}sin(x)
What is the first derivative of-e^{-x}cos(x-e^{-x}sin(x)) ?
The first derivative of-e^{-x}cos(x-e^{-x}sin(x)) is 2e^{-x}sin(x)