derivative (4x^2+1)/(x^2+5)

Lösung

ableitung von

\frac{4 x ^{2} + 1}{x ^{2} + 5}

\frac{38 x}{( x ^{2} + 5 ) ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{4 x ^{2} + 1}{x ^{2} + 5})

Wende die Quotientenregel an:

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

= \frac{\frac{d}{d x} ( 4 x ^{2} + 1 ) ( x ^{2} + 5 ) - \frac{d}{d x} ( x ^{2} + 5 ) ( 4 x ^{2} + 1 )}{( x ^{2} + 5 ) ^{2}}

\frac{d}{d x} (4 x^{2} + 1) = 8 x

\frac{d}{d x} (x^{2} + 5) = 2 x

= \frac{8 x ( x ^{2} + 5 ) - 2 x ( 4 x ^{2} + 1 )}{( x ^{2} + 5 ) ^{2}}

Multipliziere aus

8 x (x^{2} + 5) - 2 x (4 x^{2} + 1) : 38 x

= \frac{38 x}{( x ^{2} + 5 ) ^{2}}

d er i v a t i v e x e^{\frac{1}{x}}

\frac{d}{d x} (1 + 4 x^{\frac{3}{2}})

\int \frac{d ^{2} w}{2} d x

f (t) = ln (t + 1)

\frac{d}{d x} (x^{2} + 3 x + 4)