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

Lösung

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

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

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

\int (x + 4)^{2} d x

x \to 7 lim (\frac{x - 7}{3 x ^{2} - 21 x})

\frac{\partial}{\partial x} (ln (x) + z ln (y))

y^{^{''}} + 7 y^{^{'}} + 10 y = 3 e^{4 t}

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