derivative of 6(sec(x-tan(x))^{3/2})

Lösung

\frac{d}{d x} (6 (sec (x) - tan (x))^{\frac{3}{2}})

9 (sec (x) tan (x) - sec^{2} (x)) (sec (x) - tan (x))^{\frac{1}{2}}

Schritte zur Lösung

\frac{d}{d x} (6 (sec (x) - tan (x))^{\frac{3}{2}})

Entferne die Konstante:

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

= 6 \frac{d}{d x} ((sec (x) - tan (x))^{\frac{3}{2}})

Wende die Kettenregel an:

\frac{3 ( sec ( x ) - tan ( x ) ) ^{\frac{1}{2}}}{2} \frac{d}{d x} (sec (x) - tan (x))

= \frac{3 ( sec ( x ) - tan ( x ) ) ^{\frac{1}{2}}}{2} \frac{d}{d x} (sec (x) - tan (x))

\frac{d}{d x} (sec (x) - tan (x)) = sec (x) tan (x) - sec^{2} (x)

= 6 \cdot \frac{3 ( sec ( x ) - tan ( x ) ) ^{\frac{1}{2}}}{2} (sec (x) tan (x) - sec^{2} (x))

Vereinfache

6 \cdot \frac{3 ( sec ( x ) - tan ( x ) ) ^{\frac{1}{2}}}{2} (sec (x) tan (x) - sec^{2} (x)) : 9 (sec (x) tan (x) - sec^{2} (x)) (sec (x) - tan (x))^{\frac{1}{2}}

= 9 (sec (x) tan (x) - sec^{2} (x)) (sec (x) - tan (x))^{\frac{1}{2}}

a re a x^{2} - 11, 10 x, [- 11, 0] y = 0

\frac{d}{d x} (- 1 0^{3 x^{2} - 4})

\frac{d}{d x} (\frac{2}{4 x ^{3}})

x \frac{d y}{d x} = e^{y + x}

t an g e n t x^{2} + 2 x y - y^{2} + x = 27, (4, 7)