derivative of (6x^5-7x/(x^4-8))

Lösung

\frac{d}{d x} (\frac{6 x ^{5} - 7 x}{x ^{4} - 8})

\frac{6 x ^{8} - 219 x ^{4} + 56}{( x ^{4} - 8 ) ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{6 x ^{5} - 7 x}{x ^{4} - 8})

Wende die Quotientenregel an:

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

= \frac{\frac{d}{d x} ( 6 x ^{5} - 7 x ) ( x ^{4} - 8 ) - \frac{d}{d x} ( x ^{4} - 8 ) ( 6 x ^{5} - 7 x )}{( x ^{4} - 8 ) ^{2}}

\frac{d}{d x} (6 x^{5} - 7 x) = 30 x^{4} - 7

\frac{d}{d x} (x^{4} - 8) = 4 x^{3}

= \frac{( 30 x ^{4} - 7 ) ( x ^{4} - 8 ) - 4 x ^{3} ( 6 x ^{5} - 7 x )}{( x ^{4} - 8 ) ^{2}}

Multipliziere aus

(30 x^{4} - 7) (x^{4} - 8) - 4 x^{3} (6 x^{5} - 7 x) : 6 x^{8} - 219 x^{4} + 56

= \frac{6 x ^{8} - 219 x ^{4} + 56}{( x ^{4} - 8 ) ^{2}}

\int (6 e^{- 0.2 x}) d x

a re a 5 - x, 25 - x^{2}

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

x \to 4 + lim (x - 4)

d er i v a t i v e f (x) = 0.6 x^{1.5}