derivative f(x)=sin(1/(x^2))

Lösung

ableitung von

f (x) = sin (\frac{1}{x ^{2}})

- \frac{2 cos ( \frac{1}{x ^{2}} )}{x ^{3}}

Schritte zur Lösung

\frac{d}{d x} (sin (\frac{1}{x ^{2}}))

Wende die Kettenregel an:

cos (\frac{1}{x ^{2}}) \frac{d}{d x} (\frac{1}{x ^{2}})

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

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

= cos (\frac{1}{x ^{2}}) (- \frac{2}{x ^{3}})

Vereinfache

cos (\frac{1}{x ^{2}}) (- \frac{2}{x ^{3}}) : - \frac{2 cos ( \frac{1}{x ^{2}} )}{x ^{3}}

= - \frac{2 cos ( \frac{1}{x ^{2}} )}{x ^{3}}

\int \frac{cos ^{6} ( x )}{sin ^{10} ( x )} d x

y^{^{''}} + \frac{a _{1^{2}} π ^{2}}{a _{2}^{2}} a_{3}^{2} y = 0

in v erse l a pl a ce sin (s)

\int - e^{x} + sin (2 x) d x

\int_{0}^{3} cos (\frac{n x π}{3}) d x