What is the derivative of e^{0.4x}*cos(0.2x) ?

The derivative of e^{0.4x}*cos(0.2x) is 0.4e^{0.4x}cos(0.2x)-0.2e^{0.4x}sin(0.2x)

What is the first derivative of e^{0.4x}*cos(0.2x) ?

The first derivative of e^{0.4x}*cos(0.2x) is 0.4e^{0.4x}cos(0.2x)-0.2e^{0.4x}sin(0.2x)

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\frac{d}{d x} (e^{0.4 x} \cdot cos (0.2 x))

0.4 e^{0.4 x} cos (0.2 x) - 0.2 e^{0.4 x} sin (0.2 x)

Solution steps

\frac{d}{d x} (e^{0.4 x} cos (0.2 x))

Apply the Product Rule:

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

f = e^{0.4 x}, g = cos (0.2 x)

= \frac{d}{d x} (e^{0.4 x}) cos (0.2 x) + \frac{d}{d x} (cos (0.2 x)) e^{0.4 x}

\frac{d}{d x} (e^{0.4 x}) = e^{0.4 x} \cdot 0.4

\frac{d}{d x} (cos (0.2 x)) = - sin (0.2 x) \cdot 0.2

= e^{0.4 x} \cdot 0.4 cos (0.2 x) + (- sin (0.2 x) \cdot 0.2) e^{0.4 x}

Simplify

= 0.4 e^{0.4 x} cos (0.2 x) - 0.2 e^{0.4 x} sin (0.2 x)

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What is the derivative of e^{0.4x}*cos(0.2x) ?
The derivative of e^{0.4x}*cos(0.2x) is 0.4e^{0.4x}cos(0.2x)-0.2e^{0.4x}sin(0.2x)
What is the first derivative of e^{0.4x}*cos(0.2x) ?
The first derivative of e^{0.4x}*cos(0.2x) is 0.4e^{0.4x}cos(0.2x)-0.2e^{0.4x}sin(0.2x)