derivative of 1/(2cos^2(x))

Lösung

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

sec^{3} (x) sin (x)

Schritte zur Lösung

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

Entferne die Konstante:

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

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

Wende Exponentenregel an:

\frac{1}{a} = a^{- 1}

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

Wende die Kettenregel an:

- \frac{2}{( cos ( x ) ) ^{3}} \frac{d}{d x} (cos (x))

= - \frac{2}{( cos ( x ) ) ^{3}} \frac{d}{d x} (cos (x))

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

= \frac{1}{2} (- \frac{2}{( cos ( x ) ) ^{3}} (- sin (x)))

Vereinfache

\frac{1}{2} (- \frac{2}{cos ^{3} ( x )} (- sin (x))) : sec^{3} (x) sin (x)

= sec^{3} (x) sin (x)

\int (x x + 2) d x

t an g e n t y = 9 + 4 x^{2} - 2 x^{3}, (1, 11)

\frac{d}{d x} (\frac{9}{ln ( x )})

\int - 4 t d t

d er i v a t i v e f (x) = - 1 - x x^{2}