derivative f(x)= x/(x^2+196)

Lösung

ableitung von

f (x) = \frac{x}{x ^{2} + 196}

\frac{- x ^{2} + 196}{( x ^{2} + 196 ) ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{x}{x ^{2} + 196})

Wende die Quotientenregel an:

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

= \frac{\frac{d x}{d x} ( x ^{2} + 196 ) - \frac{d}{d x} ( x ^{2} + 196 ) x}{( x ^{2} + 196 ) ^{2}}

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

\frac{d}{d x} (x^{2} + 196) = 2 x

= \frac{1 \cdot ( x ^{2} + 196 ) - 2 xx}{( x ^{2} + 196 ) ^{2}}

1 \cdot (x^{2} + 196) - 2 xx = - x^{2} + 196

= \frac{- x ^{2} + 196}{( x ^{2} + 196 ) ^{2}}

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

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

\frac{\partial}{\partial x} (2 (x - a))

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\frac{d}{d x} (e^{4 x^{3}})