What is the derivative of e^{-x}(acos(x+bsin(x))) ?

The derivative of e^{-x}(acos(x+bsin(x))) is -e^{-x}(acos(x)+bsin(x))+e^{-x}(-asin(x)+bcos(x))

What is the first derivative of e^{-x}(acos(x+bsin(x))) ?

The first derivative of e^{-x}(acos(x+bsin(x))) is -e^{-x}(acos(x)+bsin(x))+e^{-x}(-asin(x)+bcos(x))

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

- e^{- x} (a cos (x) + b sin (x)) + e^{- x} (- a sin (x) + b cos (x))

Solution steps

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

Apply the Product Rule:

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

f = e^{- x}, g = a cos (x) + b sin (x)

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

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

\frac{d}{d x} (a cos (x) + b sin (x)) = - a sin (x) + b cos (x)

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

Simplify

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

x \to - \infty lim (\frac{7 x ^{4} - 14 x ^{2}}{6 x ^{5} + 3})

\frac{d}{d x} (sin (\frac{5}{2} ln (x)))

\int \frac{sin ( k t )}{a + cos ( k t )} d t

x \to 3 lim (3 x^{2} + 4 x - 1)

x \to 0 lim (\frac{x - 2}{x - 2})

What is the derivative of e^{-x}(acos(x+bsin(x))) ?
The derivative of e^{-x}(acos(x+bsin(x))) is -e^{-x}(acos(x)+bsin(x))+e^{-x}(-asin(x)+bcos(x))
What is the first derivative of e^{-x}(acos(x+bsin(x))) ?
The first derivative of e^{-x}(acos(x+bsin(x))) is -e^{-x}(acos(x)+bsin(x))+e^{-x}(-asin(x)+bcos(x))