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Beliebt Rechnen >

derivative of-2ln(cos(x))

Lösung

\frac{d}{d x} (- 2 ln (cos (x)))

Lösung

2 tan (x)

Schritte zur Lösung

\frac{d}{d x} (- 2 ln (cos (x)))

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

= - 2 \frac{d}{d x} (ln (cos (x)))

Wende die Kettenregel an:

\frac{1}{cos ( x )} \frac{d}{d x} (cos (x))

= \frac{1}{cos ( x )} \frac{d}{d x} (cos (x))

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

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

Vereinfache

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

= 2 tan (x)

Graph

Beliebte Beispiele

integral of x*e^{2x^2}

\int x \cdot e^{2 x^{2}} d x

integral from 1 to 2 of-x^2+3x-2

\int_{1}^{2} - x^{2} + 3 x - 2 d x

2x^2(dy)/(dx)+2xy=y^3

2 x^{2} \frac{d y}{d x} + 2 x y = y^{3}

integral of sqrt(36-9x^2)

\int 36 - 9 x^{2} d x

d/(ds)((1-s^2)/((s^2+1)^2))

\frac{d}{d s} (\frac{1 - s ^{2}}{( s ^{2} + 1 ) ^{2}})