derivative of x/(x^2+169)

Lösung

\frac{d}{d x} (\frac{x}{x ^{2} + 169})

\frac{- x ^{2} + 169}{( x ^{2} + 169 ) ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{x}{x ^{2} + 169})

Wende die Quotientenregel an:

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

= \frac{\frac{d x}{d x} ( x ^{2} + 169 ) - \frac{d}{d x} ( x ^{2} + 169 ) x}{( x ^{2} + 169 ) ^{2}}

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

\frac{d}{d x} (x^{2} + 169) = 2 x

= \frac{1 \cdot ( x ^{2} + 169 ) - 2 xx}{( x ^{2} + 169 ) ^{2}}

1 \cdot (x^{2} + 169) - 2 xx = - x^{2} + 169

= \frac{- x ^{2} + 169}{( x ^{2} + 169 ) ^{2}}

d er i v a t i v e y = x^{x^{3}}

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

\int \frac{2 e ^{x}}{1 - e ^{2 x}} d x

d er i v a t i v e 9 x^{2} sin (x) tan (x)

\int a cos (t) d t