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)

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\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

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

ln (3 x + 5)

f (x) = x^{2} - 4 x, at x = - 2

\frac{d}{d x} ((3 x^{2} + 2 x) (x^{4} - 3 x + 1))

y^{^{'''}} + y^{^{'}} = sec (x)

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