derivative ((x^4+9))/(x^2)

Lösung

ableitung von

\frac{( x ^{4} + 9 )}{x ^{2}}

\frac{2 ( x ^{4} - 9 )}{x ^{3}}

Schritte zur Lösung

\frac{d}{d x} (\frac{x ^{4} + 9}{x ^{2}})

Wende die Quotientenregel an:

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

= \frac{\frac{d}{d x} ( x ^{4} + 9 ) x ^{2} - \frac{d}{d x} ( x ^{2} ) ( x ^{4} + 9 )}{( x ^{2} ) ^{2}}

\frac{d}{d x} (x^{4} + 9) = 4 x^{3}

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

= \frac{4 x ^{3} x ^{2} - 2 x ( x ^{4} + 9 )}{( x ^{2} ) ^{2}}

Vereinfache

\frac{4 x ^{3} x ^{2} - 2 x ( x ^{4} + 9 )}{( x ^{2} ) ^{2}} : \frac{2 ( x ^{4} - 9 )}{x ^{3}}

= \frac{2 ( x ^{4} - 9 )}{x ^{3}}

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

\frac{d}{d a} (\frac{( a - t ^{2} )}{( b \cdot x )})

d er i v a t i v e - 12 x

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

\frac{d}{d h} (0.606 \cdot h^{3} + 0.27 \cdot h^{2} + 0.12 \cdot h)