(\partial)/(\partial x)(x/(x^2+81))

Lösung

\frac{\partial}{\partial x} (\frac{x}{x ^{2} + 81})

\frac{- x ^{2} + 81}{( x ^{2} + 81 ) ^{2}}

Schritte zur Lösung

\frac{\partial}{\partial x} (\frac{x}{x ^{2} + 81})

Wende die Quotientenregel an:

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

= \frac{\frac{\partial}{\partial x} ( x ) ( x ^{2} + 81 ) - \frac{\partial}{\partial x} ( x ^{2} + 81 ) x}{( x ^{2} + 81 ) ^{2}}

\frac{\partial}{\partial x} (x) = 1

\frac{\partial}{\partial x} (x^{2} + 81) = 2 x

= \frac{1 \cdot ( x ^{2} + 81 ) - 2 xx}{( x ^{2} + 81 ) ^{2}}

1 \cdot (x^{2} + 81) - 2 xx = - x^{2} + 81

= \frac{- x ^{2} + 81}{( x ^{2} + 81 ) ^{2}}

y^{^{'}} - 2 y = 3 x^{2}

x \to 4 lim (x^{2} - 16)

x \to - 2 lim (\frac{5 x + 3}{2 x - 9})

d er i v a t i v e (2 x^{5} - 3)^{8}

\int_{0}^{2} \frac{( x + 2 )}{( x - 4 )} d x