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

Lösung

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

- 2 x tan (x^{2} + 1)

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

= - 2 x tan (x^{2} + 1)

d er i v a t i v e f (v) = e^{2 s i n (3 v)}

\int sin (x) - cos (x) d x

n = 1 \sum \infty (- 3)^{n}

\frac{d y}{d x} = \frac{x - 3}{y + 5}

n = 1 \sum \infty 3 \cdot (\frac{1}{5})^{n}