derivative e^{t/9}sin(t/9)

Lösung

ableitung von

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

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

Schritte zur Lösung

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

Wende die Produktregel an:

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

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

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

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

\int 8 (tan (8 x)) d x

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t an g e n t x^{3}, at x = - 1