d/(d{x)}(({x)/y {z}}{{x}^2+{y}^2+{z}^2})

Lösung

\frac{d}{d x} (\frac{x y z}{x ^{2} + y ^{2} + z ^{2}})

\frac{( - x ^{2} + y ^{2} + z ^{2} ) y z}{( x ^{2} + y ^{2} + z ^{2} ) ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{x y z}{x ^{2} + y ^{2} + z ^{2}})

Entferne die Konstante:

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

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

Wende die Quotientenregel an:

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

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

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

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

= y z \frac{1 \cdot ( x ^{2} + y ^{2} + z ^{2} ) - 2 x x}{( x ^{2} + y ^{2} + z ^{2} ) ^{2}}

Vereinfache

y z \frac{1 \cdot ( x ^{2} + y ^{2} + z ^{2} ) - 2 x x}{( x ^{2} + y ^{2} + z ^{2} ) ^{2}} : \frac{( - x ^{2} + y ^{2} + z ^{2} ) y z}{( x ^{2} + y ^{2} + z ^{2} ) ^{2}}

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

x \to 5 lim (- x^{2} + 5 x - 8)

\int \frac{cos ^{2} ( x ) sin ( 2 x )}{2} d x

\int (y sin (x)) d x

s l o p e (- 3, - 8), (4, 6)

\int_{0}^{0.2} 8 e^{- 8 x} d x