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Beliebt Rechnen >

derivative sqrt(t^2+a^2)

Lösung

ableitung von

t^{2} + a^{2}

Lösung

\frac{t}{t ^{2} + a ^{2}}

Schritte zur Lösung

\frac{d}{d t} (t^{2} + a^{2})

Behandle

a

als Konstante

Wende die Kettenregel an:

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

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

\frac{d}{d t} (t^{2} + a^{2}) = 2 t

= \frac{1}{2 t ^{2} + a ^{2}} \cdot 2 t

Vereinfache

\frac{1}{2 t ^{2} + a ^{2}} \cdot 2 t : \frac{t}{t ^{2} + a ^{2}}

= \frac{t}{t ^{2} + a ^{2}}

Graph

Beliebte Beispiele

derivative of x^4e^{10x}

\frac{d}{d x} (x^{4} e^{10 x})

derivative of 8/5 x^{-2/4}

\frac{d}{d x} (\frac{8}{5} x^{- \frac{2}{4}})

tangent f(x)=x^3+2x,\at x=3

t an g e n t f (x) = x^{3} + 2 x, at x = 3

limit as x approaches 1 of 7

x \to 1 lim (7)

ma c l a u r in x^{4}