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

Lösung

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

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

Schritte zur Lösung

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

Wende die Produktregel an:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = sin (x), g = ln (x^{2} + 1)

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

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

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

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

Multipliziere Brüche:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

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

im pl i c i t \frac{d y}{d x}, tan (x - y) = \frac{y}{1 - x ^{2}}

\int cot (42 x) d x

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

\frac{d}{d x} (arcsec (\frac{x}{a}))

\int_{- \infty}^{0} \frac{1}{5 - 8 x} d x