derivative y=(x^{cot(g(x))})

Lösung

ableitung von

y = (x^{c o t (g (x))})

x^{c o t (g (x))} (- csc^{2} (g (x)) ln (x) \frac{d g}{d x} + \frac{cot ( g ( x ) )}{x})

Schritte zur Lösung

\frac{d}{d x} (x^{c o t (g (x))})

Wende Exponentenregel an:

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

x^{c o t (g (x))} = e^{c o t (g (x)) l n (x)}

= \frac{d}{d x} (e^{c o t (g (x)) l n (x)})

Wende die Kettenregel an:

e^{c o t (g (x)) l n (x)} \frac{d}{d x} (cot (g (x)) ln (x))

= e^{c o t (g (x)) l n (x)} \frac{d}{d x} (cot (g (x)) ln (x))

\frac{d}{d x} (cot (g (x)) ln (x)) = - csc^{2} (g (x)) ln (x) \frac{d g}{d x} + \frac{cot ( g ( x ) )}{x}

= e^{c o t (g (x)) l n (x)} (- csc^{2} (g (x)) ln (x) \frac{d g}{d x} + \frac{cot ( g ( x ) )}{x})

e^{c o t (g (x)) l n (x)} = x^{c o t (g (x))}

= x^{c o t (g (x))} (- csc^{2} (g (x)) ln (x) \frac{d g}{d x} + \frac{cot ( g ( x ) )}{x})

in v erse l a pl a ce \frac{( e ^{- 4 s} )}{s + 2}

\int cos^{2} (t) + sin^{2} (t) d t

x \to 8 lim (5 x - 2)

\frac{d}{d x} (A x e^{\frac{x}{2}} + B)

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