derivative (36x)/(x^2+36)

Lösung

ableitung von

\frac{36 x}{x ^{2} + 36}

\frac{36 ( - x ^{2} + 36 )}{( x ^{2} + 36 ) ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{36 x}{x ^{2} + 36})

Entferne die Konstante:

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

= 36 \frac{d}{d x} (\frac{x}{x ^{2} + 36})

Wende die Quotientenregel an:

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

= 36 \cdot \frac{\frac{d x}{d x} ( x ^{2} + 36 ) - \frac{d}{d x} ( x ^{2} + 36 ) x}{( x ^{2} + 36 ) ^{2}}

\frac{d x}{d x} = 1

\frac{d}{d x} (x^{2} + 36) = 2 x

= 36 \cdot \frac{1 \cdot ( x ^{2} + 36 ) - 2 xx}{( x ^{2} + 36 ) ^{2}}

Vereinfache

36 \cdot \frac{1 \cdot ( x ^{2} + 36 ) - 2 xx}{( x ^{2} + 36 ) ^{2}} : \frac{36 ( - x ^{2} + 36 )}{( x ^{2} + 36 ) ^{2}}

= \frac{36 ( - x ^{2} + 36 )}{( x ^{2} + 36 ) ^{2}}

\frac{d}{d x} (- 4 e^{12 x})

\int (3^{4} + x^{15}) d x

\int x^{2} a^{2} - x^{2} d x

f (x) = x^{3} - x

t an g e n t y = (2 x - 1) (x + 4), (1, 5)