derivative [tan(x^{2/3})]^3

Lösung

ableitung von

[tan (x^{\frac{2}{3}})]^{3}

\frac{2 sec ^{2} ( x ^{\frac{2}{3}} ) tan ^{2} ( x ^{\frac{2}{3}} )}{x ^{\frac{1}{3}}}

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

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

= 3 (tan (x^{\frac{2}{3}}))^{2} \frac{2 sec ^{2} ( x ^{\frac{2}{3}} )}{3 x ^{\frac{1}{3}}}

Vereinfache

3 tan^{2} (x^{\frac{2}{3}}) \frac{2 sec ^{2} ( x ^{\frac{2}{3}} )}{3 x ^{\frac{1}{3}}} : \frac{2 sec ^{2} ( x ^{\frac{2}{3}} ) tan ^{2} ( x ^{\frac{2}{3}} )}{x ^{\frac{1}{3}}}

= \frac{2 sec ^{2} ( x ^{\frac{2}{3}} ) tan ^{2} ( x ^{\frac{2}{3}} )}{x ^{\frac{1}{3}}}

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

d er i v a t i v e f (t) = 7 + 10 x

\int \frac{1}{5 x - 3} d x

h \to 0 lim (\frac{( 2 ^{h} - 1 )}{h})

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