derivative of (x^2/(3x+7))

Lösung

\frac{d}{d x} (\frac{x ^{2}}{3 x + 7})

\frac{3 x ^{2} + 14 x}{( 3 x + 7 ) ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{x ^{2}}{3 x + 7})

Wende die Quotientenregel an:

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

= \frac{\frac{d}{d x} ( x ^{2} ) ( 3 x + 7 ) - \frac{d}{d x} ( 3 x + 7 ) x ^{2}}{( 3 x + 7 ) ^{2}}

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

\frac{d}{d x} (3 x + 7) = 3

= \frac{2 x ( 3 x + 7 ) - 3 x ^{2}}{( 3 x + 7 ) ^{2}}

Multipliziere aus

2 x (3 x + 7) - 3 x^{2} : 3 x^{2} + 14 x

= \frac{3 x ^{2} + 14 x}{( 3 x + 7 ) ^{2}}

d er i v a t i v e x^{\frac{1}{3}} - 1

\frac{d}{d t} (\frac{1}{( t + 1 ) ^{2}})

\int 3 x y^{2} d y

\frac{\partial}{\partial x} (e^{e^{y} (1 + e^{x}) - 2})

a re a x^{2} - 2, - (x - 1)^{2} + 3