What is the derivative of e^{x/8}cos(x/8) ?

The derivative of e^{x/8}cos(x/8) is 1/8 e^{x/8}cos(x/8)-1/8 e^{x/8}sin(x/8)

What is the first derivative of e^{x/8}cos(x/8) ?

The first derivative of e^{x/8}cos(x/8) is 1/8 e^{x/8}cos(x/8)-1/8 e^{x/8}sin(x/8)

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\frac{d}{d x} (e^{\frac{x}{8}} cos (\frac{x}{8}))

\frac{1}{8} e^{\frac{x}{8}} cos (\frac{x}{8}) - \frac{1}{8} e^{\frac{x}{8}} sin (\frac{x}{8})

Solution steps

\frac{d}{d x} (e^{\frac{x}{8}} cos (\frac{x}{8}))

Apply the Product Rule:

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

f = e^{\frac{x}{8}}, g = cos (\frac{x}{8})

= \frac{d}{d x} (e^{\frac{x}{8}}) cos (\frac{x}{8}) + \frac{d}{d x} (cos (\frac{x}{8})) e^{\frac{x}{8}}

\frac{d}{d x} (e^{\frac{x}{8}}) = e^{\frac{x}{8}} \frac{1}{8}

\frac{d}{d x} (cos (\frac{x}{8})) = - sin (\frac{x}{8}) \frac{1}{8}

= e^{\frac{x}{8}} \frac{1}{8} cos (\frac{x}{8}) + (- sin (\frac{x}{8}) \frac{1}{8}) e^{\frac{x}{8}}

Simplify

= \frac{1}{8} e^{\frac{x}{8}} cos (\frac{x}{8}) - \frac{1}{8} e^{\frac{x}{8}} sin (\frac{x}{8})

What is the derivative of e^{x/8}cos(x/8) ?
The derivative of e^{x/8}cos(x/8) is 1/8 e^{x/8}cos(x/8)-1/8 e^{x/8}sin(x/8)
What is the first derivative of e^{x/8}cos(x/8) ?
The first derivative of e^{x/8}cos(x/8) is 1/8 e^{x/8}cos(x/8)-1/8 e^{x/8}sin(x/8)