derivative of sin^2((x+2/(x+1)))

Lösung

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

- \frac{sin ( \frac{2 ( 2 + x )}{1 + x} )}{( 1 + x ) ^{2}}

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

y^{^{'}} = ln (x) y + x^{x}

\frac{d}{d x} (sin (x) + cos (x))

\int_{0}^{2} x^{2} (x^{3} + 1)^{\frac{3}{2}} d x

a re a 3 x^{2}, x^{2} + 4, - 2, 2

d er i v a t i v e ln (\frac{x}{x ^{2} + 6})