derivative of 3cot(2xsec(2x))

Lösung

\frac{d}{d x} (3 cot (2 x) sec (2 x))

3 (- 2 csc^{2} (2 x) sec (2 x) + 2 sec (2 x) tan (2 x) cot (2 x))

Schritte zur Lösung

\frac{d}{d x} (3 cot (2 x) sec (2 x))

Entferne die Konstante:

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

= 3 \frac{d}{d x} (cot (2 x) sec (2 x))

Wende die Produktregel an:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = cot (2 x), g = sec (2 x)

= 3 (\frac{d}{d x} (cot (2 x)) sec (2 x) + \frac{d}{d x} (sec (2 x)) cot (2 x))

\frac{d}{d x} (cot (2 x)) = - csc^{2} (2 x) \cdot 2

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

= 3 ((- csc^{2} (2 x) \cdot 2) sec (2 x) + sec (2 x) tan (2 x) \cdot 2 cot (2 x))

Vereinfache

= 3 (- 2 csc^{2} (2 x) sec (2 x) + 2 sec (2 x) tan (2 x) cot (2 x))

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

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

e x p an d \frac{6}{( 1 - x ) ^{3}}

\frac{d}{d t} (\frac{t ^{4}}{4})

\frac{d}{d x} (x^{- \frac{2}{5}})