d/(dt)(5tsin(4pit))

Lösung

\frac{d}{d t} (5 t sin (4 π t))

5 (sin (4 π t) + 4 π t cos (4 π t))

Schritte zur Lösung

\frac{d}{d t} (5 t sin (4 π t))

Entferne die Konstante:

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

= 5 \frac{d}{d t} (t sin (4 π t))

Wende die Produktregel an:

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

f = t, g = sin (4 π t)

= 5 (\frac{d t}{d t} sin (4 π t) + \frac{d}{d t} (sin (4 π t)) t)

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

\frac{d}{d t} (sin (4 π t)) = cos (4 π t) \cdot 4 π

= 5 (1 \cdot sin (4 π t) + cos (4 π t) \cdot 4 π t)

Vereinfache

= 5 (sin (4 π t) + 4 π t cos (4 π t))

\frac{d}{d x} (2 x + 2)

\int \frac{( ln ( x ) + 7 ) ^{3}}{x} d x

\frac{d}{d x} (3 x^{2} - 4 x + 10)

\int (\frac{x ^{3}}{3} - \frac{3}{x ^{3}}) d x

a re a y = x^{3} + x^{2} + x - 1, y = x^{3} + 5