derivative of 1/(3x^2-5/(2x)+8x-6)

Lösung

\frac{d}{d x} (\frac{1}{3 x ^{2}} - \frac{5}{2 x} + 8 x - 6)

\frac{5}{2 x ^{2}} - \frac{2}{3 x ^{3}} + 8

Schritte zur Lösung

\frac{d}{d x} (\frac{1}{3 x ^{2}} - \frac{5}{2 x} + 8 x - 6)

Wende die Summen-/Differenzregel an:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (\frac{1}{3 x ^{2}}) - \frac{d}{d x} (\frac{5}{2 x}) + \frac{d}{d x} (8 x) - \frac{d}{d x} (6)

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

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

\frac{d}{d x} (8 x) = 8

\frac{d}{d x} (6) = 0

= - \frac{2}{3 x ^{3}} - (- \frac{5}{2 x ^{2}}) + 8 - 0

Vereinfache

= \frac{5}{2 x ^{2}} - \frac{2}{3 x ^{3}} + 8

\frac{d}{d x} (2 cos (- x))

in v erse l a pl a ce \frac{( x )}{( x + 2 ) ( x - 3 )}

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

x \frac{d y}{d x} = y^{2} - y

\int_{1}^{4} t^{- \frac{3}{2}} d t