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Beliebt Rechnen >

derivative g(t)=sqrt(3t+\sqrt{5t+9)}

Lösung

ableitung von

g (t) = 3 t + 5 t + 9

Lösung

\frac{6 5 t + 9 + 5}{4 5 t + 9 3 t + 5 t + 9}

Schritte zur Lösung

\frac{d}{d t} (3 t + 5 t + 9)

Wende die Kettenregel an:

\frac{1}{2 3 t + 5 t + 9} \frac{d}{d t} (3 t + 5 t + 9)

= \frac{1}{2 3 t + 5 t + 9} \frac{d}{d t} (3 t + 5 t + 9)

\frac{d}{d t} (3 t + 5 t + 9) = 3 + \frac{5}{2 5 t + 9}

= \frac{1}{2 3 t + 5 t + 9} (3 + \frac{5}{2 5 t + 9})

Vereinfache

\frac{1}{2 3 t + 5 t + 9} (3 + \frac{5}{2 5 t + 9}) : \frac{6 5 t + 9 + 5}{4 5 t + 9 3 t + 5 t + 9}

= \frac{6 5 t + 9 + 5}{4 5 t + 9 3 t + 5 t + 9}

Graph

Beliebte Beispiele

(2x+8y)dx+(8x+4y)dy=0

(2 x + 8 y) d x + (8 x + 4 y) d y = 0

derivative f(x)= x/(x^2-5)

d er i v a t i v e f (x) = \frac{x}{x ^{2} - 5}

limit as x approaches-1 of (x^3+1)/(x+1)

x \to - 1 lim (\frac{x ^{3} + 1}{x + 1})

tangent f(x)= 4/(3x-1),\at x=3

t an g e n t f (x) = \frac{4}{3 x - 1}, at x = 3

derivative ln(4x^3+5x^2+2x+5)

d er i v a t i v e ln (4 x^{3} + 5 x^{2} + 2 x + 5)