derivative of e^{x^2\sqrt[3]{4x-1}}

Lösung

\frac{d}{d x} (e^{x^{2} 3 4 x - 1})

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

Schritte zur Lösung

\frac{d}{d x} (e^{x^{2} 3 4 x - 1})

Wende die Kettenregel an:

e^{x^{2} 3 4 x - 1} \frac{d}{d x} (x^{2} 3 4 x - 1)

= e^{x^{2} 3 4 x - 1} \frac{d}{d x} (x^{2} 3 4 x - 1)

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

= e^{x^{2} 3 4 x - 1} (2 x 3 4 x - 1 + \frac{4 x ^{2}}{3 ( 4 x - 1 ) ^{\frac{2}{3}}})

\frac{d}{d x} (e^{\frac{x}{6}})

\int \frac{1}{1 + e ^{- t}} d t

\int \frac{x ^{2}}{x ^{2} + 81} d x

\frac{y ^{^{'}} - e ^{- t} + 5}{y} = - 5, y (0) = - 4

s l o p e (5, - 1), (- 3, 4)