What is the derivative of e^{-7x}cos(7x) ?

The derivative of e^{-7x}cos(7x) is -7e^{-7x}cos(7x)-7e^{-7x}sin(7x)

What is the first derivative of e^{-7x}cos(7x) ?

The first derivative of e^{-7x}cos(7x) is -7e^{-7x}cos(7x)-7e^{-7x}sin(7x)

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\frac{d}{d x} (e^{- 7 x} cos (7 x))

- 7 e^{- 7 x} cos (7 x) - 7 e^{- 7 x} sin (7 x)

Solution steps

\frac{d}{d x} (e^{- 7 x} cos (7 x))

Apply the Product Rule:

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

f = e^{- 7 x}, g = cos (7 x)

= \frac{d}{d x} (e^{- 7 x}) cos (7 x) + \frac{d}{d x} (cos (7 x)) e^{- 7 x}

\frac{d}{d x} (e^{- 7 x}) = - 7 e^{- 7 x}

\frac{d}{d x} (cos (7 x)) = - sin (7 x) \cdot 7

= (- 7 e^{- 7 x}) cos (7 x) + (- sin (7 x) \cdot 7) e^{- 7 x}

Simplify

= - 7 e^{- 7 x} cos (7 x) - 7 e^{- 7 x} sin (7 x)

y = 2 x^{2} + 5, (- 1, 7)

f (x) = x^{2} e^{x} - 2 x e^{x} + 2 e^{x}

\int tan^{4} (5 t) d t

\int \frac{1 + 3 x}{( 1 - x ) ( 3 x - 5 )} d x

\int e^{7 t} d t

What is the derivative of e^{-7x}cos(7x) ?
The derivative of e^{-7x}cos(7x) is -7e^{-7x}cos(7x)-7e^{-7x}sin(7x)
What is the first derivative of e^{-7x}cos(7x) ?
The first derivative of e^{-7x}cos(7x) is -7e^{-7x}cos(7x)-7e^{-7x}sin(7x)