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Beliebt Rechnen >

derivative (sqrt(t))/(1+t^2)

Lösung

ableitung von

\frac{t}{1 + t ^{2}}

Lösung

\frac{1 - 3 t ^{2}}{2 t ( 1 + t ^{2} ) ^{2}}

Schritte zur Lösung

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

Wende die Quotientenregel an:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

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

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

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

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

Vereinfache

\frac{\frac{1}{2 t} ( 1 + t ^{2} ) - 2 t t}{( 1 + t ^{2} ) ^{2}} : \frac{1 - 3 t ^{2}}{2 t ( 1 + t ^{2} ) ^{2}}

= \frac{1 - 3 t ^{2}}{2 t ( 1 + t ^{2} ) ^{2}}

Graph

Beliebte Beispiele

integral of (x^4)/(4sqrt(x^2+1))

\int \frac{x ^{4}}{4 x ^{2} + 1} d x

fläche x^2+1,x,[-1,2]

a re a x^{2} + 1, x, [- 1, 2]

(d^2)/(dx^2)(3xe^x)

\frac{d ^{2}}{d x ^{2}} (3 x e^{x})

integral of (x-3)/((x-5)x^2)

\int \frac{x - 3}{( x - 5 ) x ^{2}} d x

steigung (1.1)(3.4)

s l o p e (1.1) (3.4)