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}cos(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}cos(x)

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

- 2 e^{- x} cos (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} cos (x)

\frac{d y}{d x} + 3 y = x^{2}

\int \frac{tan ^{3} ( θ )}{cos ^{2} ( θ )} d θ

f (x) = x^{2} - 3 x + 2, at x = 1

(x + 9) (9 x + 7)

\int x 7 - x^{2} d x

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}cos(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}cos(x)