What is the derivative of e^{t/9}cos(t/9) ?

The derivative of e^{t/9}cos(t/9) is 1/9 e^{t/9}cos(t/9)-1/9 e^{t/9}sin(t/9)

What is the first derivative of e^{t/9}cos(t/9) ?

The first derivative of e^{t/9}cos(t/9) is 1/9 e^{t/9}cos(t/9)-1/9 e^{t/9}sin(t/9)

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derivative of

e^{\frac{t}{9}} cos (\frac{t}{9})

\frac{1}{9} e^{\frac{t}{9}} cos (\frac{t}{9}) - \frac{1}{9} e^{\frac{t}{9}} sin (\frac{t}{9})

Solution steps

\frac{d}{d t} (e^{\frac{t}{9}} cos (\frac{t}{9}))

Apply the Product Rule:

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

f = e^{\frac{t}{9}}, g = cos (\frac{t}{9})

= \frac{d}{d t} (e^{\frac{t}{9}}) cos (\frac{t}{9}) + \frac{d}{d t} (cos (\frac{t}{9})) e^{\frac{t}{9}}

\frac{d}{d t} (e^{\frac{t}{9}}) = e^{\frac{t}{9}} \frac{1}{9}

\frac{d}{d t} (cos (\frac{t}{9})) = - sin (\frac{t}{9}) \frac{1}{9}

= e^{\frac{t}{9}} \frac{1}{9} cos (\frac{t}{9}) + (- sin (\frac{t}{9}) \frac{1}{9}) e^{\frac{t}{9}}

Simplify

= \frac{1}{9} e^{\frac{t}{9}} cos (\frac{t}{9}) - \frac{1}{9} e^{\frac{t}{9}} sin (\frac{t}{9})

\int \frac{8 x + 1}{x ^{2} + 1} d x

f (x) = \frac{8}{x}, at x = 5

y^{^{''}} + y = 9 sin (x)

40 ln (3 x + 1) - \frac{x}{3}

y^{^{''}} - 7 y^{^{'}} + 7 y = 0

What is the derivative of e^{t/9}cos(t/9) ?
The derivative of e^{t/9}cos(t/9) is 1/9 e^{t/9}cos(t/9)-1/9 e^{t/9}sin(t/9)
What is the first derivative of e^{t/9}cos(t/9) ?
The first derivative of e^{t/9}cos(t/9) is 1/9 e^{t/9}cos(t/9)-1/9 e^{t/9}sin(t/9)