What is the derivative of e^{-5x}cos(3x) ?

The derivative of e^{-5x}cos(3x) is -5e^{-5x}cos(3x)-3e^{-5x}sin(3x)

What is the first derivative of e^{-5x}cos(3x) ?

The first derivative of e^{-5x}cos(3x) is -5e^{-5x}cos(3x)-3e^{-5x}sin(3x)

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\frac{d}{d x} (e^{- 5 x} cos (3 x))

- 5 e^{- 5 x} cos (3 x) - 3 e^{- 5 x} sin (3 x)

Solution steps

\frac{d}{d x} (e^{- 5 x} cos (3 x))

Apply the Product Rule:

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

f = e^{- 5 x}, g = cos (3 x)

= \frac{d}{d x} (e^{- 5 x}) cos (3 x) + \frac{d}{d x} (cos (3 x)) e^{- 5 x}

\frac{d}{d x} (e^{- 5 x}) = - 5 e^{- 5 x}

\frac{d}{d x} (cos (3 x)) = - sin (3 x) \cdot 3

= (- 5 e^{- 5 x}) cos (3 x) + (- sin (3 x) \cdot 3) e^{- 5 x}

Simplify

= - 5 e^{- 5 x} cos (3 x) - 3 e^{- 5 x} sin (3 x)

\int ln (7 x + 1) d x

\frac{d}{d x} ((3 x^{5} - 1) (2 - x^{4}))

y = x x + 1

\int 2 x^{3} x^{2} - 1 d x

\int 7 e^{- 0.2 x} d x

What is the derivative of e^{-5x}cos(3x) ?
The derivative of e^{-5x}cos(3x) is -5e^{-5x}cos(3x)-3e^{-5x}sin(3x)
What is the first derivative of e^{-5x}cos(3x) ?
The first derivative of e^{-5x}cos(3x) is -5e^{-5x}cos(3x)-3e^{-5x}sin(3x)