derivative of \sqrt[x-2]{2}

Lösung

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

- \frac{ln ( 2 ) e ^{\frac{l n ( 2 )}{x - 2}}}{( x - 2 ) ^{2}}

Schritte zur Lösung

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

Wende Exponentenregel an:

a^{b} = e^{b l n (a)}

x - 2 2 = e^{\frac{1}{x - 2} l n (2)}

= \frac{d}{d x} (e^{\frac{1}{x - 2} l n (2)})

Wende die Kettenregel an:

e^{\frac{1}{x - 2} l n (2)} \frac{d}{d x} (\frac{1}{x - 2} ln (2))

= e^{\frac{1}{x - 2} l n (2)} \frac{d}{d x} (\frac{1}{x - 2} ln (2))

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

= e^{\frac{1}{x - 2} l n (2)} (- \frac{ln ( 2 )}{( x - 2 ) ^{2}})

Vereinfache

e^{\frac{1}{x - 2} l n (2)} (- \frac{ln ( 2 )}{( x - 2 ) ^{2}}) : - \frac{ln ( 2 ) e ^{\frac{l n ( 2 )}{x - 2}}}{( x - 2 ) ^{2}}

= - \frac{ln ( 2 ) e ^{\frac{l n ( 2 )}{x - 2}}}{( x - 2 ) ^{2}}

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

(t^{2} + 1) \frac{d y}{d t} = 2 y

\frac{\partial}{\partial x} (x^{8} + 8 x y^{7})

\int 1 d x^{3}

f (x) = \frac{x ^{2}}{ln ( x )}