derivative of 1/({g(x)(x)^2(x)})

Lösung

\frac{d}{d x} (\frac{1}{g ( x ) ( x ) ^{2} ( x )})

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

Schritte zur Lösung

\frac{d}{d x} (\frac{1}{g ( x ) ( x ) ^{2} ( x )})

Wende Exponentenregel an:

\frac{1}{a} = a^{- 1}

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

\int \frac{( 4 x - 3 )}{x + 1} d x

x \to 0 lim (- (e^{\frac{1}{x}}))

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

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

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