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

Lösung

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

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

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

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

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

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

Multipliziere aus

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

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

d er i v a t i v e f (x) = \frac{2 - x ^{2}}{3 + x ^{2}}

n = 1 \sum \infty arctan (18 n)

n = 0 \sum \infty (1.1)^{n}

d er i v a t i v e y = arctan (x^{2} + 1)

\int \frac{1}{( 2 - x ) ( 3 - x )} d x