What is the derivative of 20e^{-4x}cos(50x) ?

The derivative of 20e^{-4x}cos(50x) is 20(-4e^{-4x}cos(50x)-50e^{-4x}sin(50x))

What is the first derivative of 20e^{-4x}cos(50x) ?

The first derivative of 20e^{-4x}cos(50x) is 20(-4e^{-4x}cos(50x)-50e^{-4x}sin(50x))

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\frac{d}{d x} (20 e^{- 4 x} cos (50 x))

20 (- 4 e^{- 4 x} cos (50 x) - 50 e^{- 4 x} sin (50 x))

Solution steps

\frac{d}{d x} (20 e^{- 4 x} cos (50 x))

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= 20 \frac{d}{d x} (e^{- 4 x} cos (50 x))

Apply the Product Rule:

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

f = e^{- 4 x}, g = cos (50 x)

= 20 (\frac{d}{d x} (e^{- 4 x}) cos (50 x) + \frac{d}{d x} (cos (50 x)) e^{- 4 x})

\frac{d}{d x} (e^{- 4 x}) = - 4 e^{- 4 x}

\frac{d}{d x} (cos (50 x)) = - sin (50 x) \cdot 50

= 20 ((- 4 e^{- 4 x}) cos (50 x) + (- sin (50 x) \cdot 50) e^{- 4 x})

Simplify

= 20 (- 4 e^{- 4 x} cos (50 x) - 50 e^{- 4 x} sin (50 x))

\frac{\partial}{\partial x} (x y^{2} - 2 x y - 2 x^{2} - 3 x)

\frac{d y}{d x} = y^{2} e^{- 2 x}

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

e^{m x}

What is the derivative of 20e^{-4x}cos(50x) ?
The derivative of 20e^{-4x}cos(50x) is 20(-4e^{-4x}cos(50x)-50e^{-4x}sin(50x))
What is the first derivative of 20e^{-4x}cos(50x) ?
The first derivative of 20e^{-4x}cos(50x) is 20(-4e^{-4x}cos(50x)-50e^{-4x}sin(50x))