derivative f(x)=sin(x)ln(x^2+1)

Lösung

ableitung von

f (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}

x \to π lim (9 cot (x))

d er i v a t i v e y = ln (x^{6})

x \to 0 lim ((e^{x} - x)^{\frac{1}{x}})

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

\int_{0}^{9} π (x - 1)^{2} d x