derivative of sqrt((x^3-2x^{x^2-3)})

Lösung

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

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

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

\frac{1}{2 ( x ^{3} - 2 x ) ^{x^{2} - 3}} (2 x ln (x^{3} - 2 x) + \frac{( 3 x ^{2} - 2 ) ( x ^{2} - 3 )}{x ^{3} - 2 x}) (x^{3} - 2 x)^{x^{2} - 3} : \frac{( 2 x ln ( x ^{3} - 2 x ) ( x ^{3} - 2 x ) + ( 3 x ^{2} - 2 ) ( x ^{2} - 3 ) ) ( x ^{3} - 2 x ) ^{x^{2} - 4}}{2 ( x ^{3} - 2 x ) ^{x^{2} - 3}}

= \frac{( 2 x ln ( x ^{3} - 2 x ) ( x ^{3} - 2 x ) + ( 3 x ^{2} - 2 ) ( x ^{2} - 3 ) ) ( x ^{3} - 2 x ) ^{x^{2} - 4}}{2 ( x ^{3} - 2 x ) ^{x^{2} - 3}}

\frac{d}{d x} (x^{2} e^{x} sin (x))

d er i v a t i v e f (x) = \frac{x + 9}{x ^{2} - 7 x + 1}

\int x \cdot sin (x^{2}) d x

\int_{- 2}^{2} x^{2} 1 + 4 x^{2} d x

\int 5 sin (6 π x) d x