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Beliebt Rechnen >

derivative f(t)=(1+sqrt(t))(2t^2-7)

Lösung

ableitung von

f (t) = (1 + t) (2 t^{2} - 7)

Lösung

\frac{10 t ^{2} + 8 t t - 7}{2 t}

Schritte zur Lösung

\frac{d}{d t} ((1 + t) (2 t^{2} - 7))

Wende die Produktregel an:

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

f = 1 + t, g = 2 t^{2} - 7

= \frac{d}{d t} (1 + t) (2 t^{2} - 7) + \frac{d}{d t} (2 t^{2} - 7) (1 + t)

\frac{d}{d t} (1 + t) = \frac{1}{2 t}

\frac{d}{d t} (2 t^{2} - 7) = 4 t

= \frac{1}{2 t} (2 t^{2} - 7) + 4 t (1 + t)

Vereinfache

\frac{1}{2 t} (2 t^{2} - 7) + 4 t (1 + t) : \frac{10 t ^{2} + 8 t t - 7}{2 t}

= \frac{10 t ^{2} + 8 t t - 7}{2 t}

Graph

Beliebte Beispiele

derivative f(x)=(e^{x^2})/(x^3)

d er i v a t i v e f (x) = \frac{e ^{x^{2}}}{x ^{3}}

derivative f(x)=x^3-12x

d er i v a t i v e f (x) = x^{3} - 12 x

\frac{d}{d z} (cos (z))

limit as x approaches 0 of pi

x \to 0 lim (π)

derivative y=ln((7+e^x)/(7-e^x))

d er i v a t i v e y = ln (\frac{7 + e ^{x}}{7 - e ^{x}})