d/(dt)(t/(10)sin(5t))

Lösung

\frac{d}{d t} (\frac{t}{10} sin (5 t))

\frac{1}{10} (sin (5 t) + 5 t cos (5 t))

Schritte zur Lösung

\frac{d}{d t} (\frac{t}{10} sin (5 t))

Entferne die Konstante:

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

= \frac{1}{10} \frac{d}{d t} (t sin (5 t))

Wende die Produktregel an:

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

f = t, g = sin (5 t)

= \frac{1}{10} (\frac{d t}{d t} sin (5 t) + \frac{d}{d t} (sin (5 t)) t)

\frac{d t}{d t} = 1

\frac{d}{d t} (sin (5 t)) = cos (5 t) \cdot 5

= \frac{1}{10} (1 \cdot sin (5 t) + cos (5 t) \cdot 5 t)

Vereinfache

= \frac{1}{10} (sin (5 t) + 5 t cos (5 t))

(1 + x^{2}) d y + (x y + x^{3} + x) d x = 0

\frac{d y}{d x} = \frac{( 6 x - 2 x y ^{3} )}{y ^{2}}

t an g e n t 2 x^{2} + 3 x - 2

d er i v a t i v e f (t) = \frac{6 t + 38}{t + 9}

\int_{1}^{6} \frac{x ^{2} + 1}{7 x - x ^{2}} d x