derivative x/(x^2+16)

Lösung

ableitung von

\frac{x}{x ^{2} + 16}

\frac{- x ^{2} + 16}{( x ^{2} + 16 ) ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{x}{x ^{2} + 16})

Wende die Quotientenregel an:

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

= \frac{\frac{d x}{d x} ( x ^{2} + 16 ) - \frac{d}{d x} ( x ^{2} + 16 ) x}{( x ^{2} + 16 ) ^{2}}

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

\frac{d}{d x} (x^{2} + 16) = 2 x

= \frac{1 \cdot ( x ^{2} + 16 ) - 2 xx}{( x ^{2} + 16 ) ^{2}}

1 \cdot (x^{2} + 16) - 2 xx = - x^{2} + 16

= \frac{- x ^{2} + 16}{( x ^{2} + 16 ) ^{2}}

\int \frac{x ^{2} - 4}{x - 2} d x

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\int x^{2} ln (x^{3}) d x

x \to - 1 - lim (x^{3} + 2 x^{2} + 1)

\int x^{4} ln (5 x) d x