derivative f(x)=(45)/(0.01x^2+1)

Lösung

ableitung von

f (x) = \frac{45}{0.01 x ^{2} + 1}

- \frac{0.9 x}{( 0.01 x ^{2} + 1 ) ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{45}{0.01 x ^{2} + 1})

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

= 45 \frac{d}{d x} (\frac{1}{0.01 x ^{2} + 1})

Wende Exponentenregel an:

\frac{1}{a} = a^{- 1}

= 45 \frac{d}{d x} ((0.01 x^{2} + 1)^{- 1})

Wende die Kettenregel an:

- \frac{1}{( 0.01 x ^{2} + 1 ) ^{2}} \frac{d}{d x} (0.01 x^{2} + 1)

= - \frac{1}{( 0.01 x ^{2} + 1 ) ^{2}} \frac{d}{d x} (0.01 x^{2} + 1)

\frac{d}{d x} (0.01 x^{2} + 1) = 0.02 x

= 45 (- \frac{1}{( 0.01 x ^{2} + 1 ) ^{2}} \cdot 0.02 x)

Vereinfache

45 (- \frac{1}{( 0.01 x ^{2} + 1 ) ^{2}} \cdot 0.02 x) : - \frac{0.9 x}{( 0.01 x ^{2} + 1 ) ^{2}}

= - \frac{0.9 x}{( 0.01 x ^{2} + 1 ) ^{2}}

l a pl a ce t r an s f or m cos^{2} (5 t)

x^{^{''''}} + 8 x^{^{''}} + 16 x = 0

25 y^{^{''}} + 9 y = 0

d er i v a t i v e \frac{1}{( x + 1 ) ^{2}}

\frac{d y}{d x} = \frac{( x - 2 )}{x}