derivative of sqrt(sin(\sqrt{1+x^2)})

Lösung

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

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

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

\frac{d}{d x} (x^{3} + 6 x^{2} - 15 x)

\int 2 e^{- 2 x} (x^{2} - 2 x + 1) d x

n = 0 \sum \infty \frac{2 ^{n} z ^{n}}{n}

\frac{\partial}{\partial z} (2 x z^{2})

t an g e n t y = 2 x - 2 x^{2}, at x = - 1.5