derivative of x^{ln(x^2+1})

Lösung

\frac{d}{d x} (x^{l n (x^{2} + 1)})

(\frac{2 x ln ( x )}{x ^{2} + 1} + \frac{ln ( x ^{2} + 1 )}{x}) (x^{2} + 1)^{l n (x)}

Schritte zur Lösung

\frac{d}{d x} (x^{l n (x^{2} + 1)})

Wende Exponentenregel an:

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

x^{l n (x^{2} + 1)} = e^{l n (x^{2} + 1) l n (x)}

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

Wende die Kettenregel an:

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

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

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

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

e^{l n (x^{2} + 1) l n (x)} = (x^{2} + 1)^{l n (x)}

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

\frac{d ^{2}}{d x ^{2}} (e^{s i n (x)})

\frac{d}{d x} ((sin (y)) x^{2})

x \to 5 lim (h (x))

y^{^{'}} + 5 (tan (5 x)) y = - 8 (cos (5 x))

l a pl a ce t r an s f or m 1 - cos (7 t)