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Beliebt Rechnen >

derivative x=tsin(t)

Lösung

ableitung von

x = t sin (t)

Lösung

sin (t) + t cos (t)

Schritte zur Lösung

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

Wende die Produktregel an:

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

f = t, g = sin (t)

= \frac{d t}{d t} sin (t) + \frac{d}{d t} (sin (t)) t

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

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

= 1 \cdot sin (t) + cos (t) t

Vereinfache

= sin (t) + t cos (t)

Graph

Beliebte Beispiele

derivative 8e^t

d er i v a t i v e 8 e^{t}

limit as x approaches 0-of x^2sin(1/x)

x \to 0 - lim (x^{2} sin (\frac{1}{x}))

integral of e^x(1/2 x^2+x)

\int e^{x} (\frac{1}{2} x^{2} + x) d x

t y^{^{'}} = y^{2} + 1

integral of xcos(bx)

\int x cos (b x) d x