derivative x^2log_{10}(1/x)

Lösung

ableitung von

x^{2} lo g_{10} (\frac{1}{x})

- \frac{x + 2 x ln ( x )}{ln ( 10 )}

Schritte zur Lösung

\frac{d}{d x} (x^{2} lo g_{10} (\frac{1}{x}))

Vereinfache

x^{2} lo g_{10} (\frac{1}{x}) : - x^{2} lo g_{10} (x)

= \frac{d}{d x} (- x^{2} lo g_{10} (x))

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

= - \frac{d}{d x} (x^{2} lo g_{10} (x))

Wende die Produktregel an:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x^{2}, g = lo g_{10} (x)

= - (\frac{d}{d x} (x^{2}) lo g_{10} (x) + \frac{d}{d x} (lo g_{10} (x)) x^{2})

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

\frac{d}{d x} (lo g_{10} (x)) = \frac{1}{x ln ( 10 )}

= - (2 x lo g_{10} (x) + \frac{1}{x ln ( 10 )} x^{2})

Vereinfache

- (2 x lo g_{10} (x) + \frac{1}{x ln ( 10 )} x^{2}) : - \frac{x + 2 x ln ( x )}{ln ( 10 )}

= - \frac{x + 2 x ln ( x )}{ln ( 10 )}

d er i v a t i v e \frac{1}{( 1 - x ^{2} )}

d er i v a t i v e sin (x) + ln (x^{2}) + e^{2} x

d er i v a t i v e 6 x^{\frac{1}{3}}

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

d er i v a t i v e (5 x + 2)^{7}