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

Lösung

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

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

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

\int 4 x^{6} - 2 x^{3} + 7 x - 4 d x

\int_{2}^{5} \frac{1}{x ^{2}} d x

\int_{0}^{2} \frac{( 4 x + 3 )}{x ^{4}} d x

\frac{d}{d x} (a sin^{3} (\frac{x}{3}))

y^{^{'}} + \frac{y}{x} = \frac{e ^{x}}{x}