derivative of 10sec(2xtan(2x))

Lösung

\frac{d}{d x} (10 sec (2 x) tan (2 x))

10 (2 tan^{2} (2 x) sec (2 x) + 2 sec^{3} (2 x))

Schritte zur Lösung

\frac{d}{d x} (10 sec (2 x) tan (2 x))

Entferne die Konstante:

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

= 10 \frac{d}{d x} (sec (2 x) tan (2 x))

Wende die Produktregel an:

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

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

= 10 (\frac{d}{d x} (sec (2 x)) tan (2 x) + \frac{d}{d x} (tan (2 x)) sec (2 x))

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

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

= 10 (sec (2 x) tan (2 x) \cdot 2 tan (2 x) + sec^{2} (2 x) \cdot 2 sec (2 x))

Vereinfache

10 (sec (2 x) tan (2 x) \cdot 2 tan (2 x) + sec^{2} (2 x) \cdot 2 sec (2 x)) : 10 (2 tan^{2} (2 x) sec (2 x) + 2 sec^{3} (2 x))

= 10 (2 tan^{2} (2 x) sec (2 x) + 2 sec^{3} (2 x))

y^{^{'}} = - \frac{2 t ( 1 + y ^{2} )}{y}

\int 6 x^{2} - 2 x + 8 d x

\frac{d}{d v} (2 uv)

\int \frac{ln ^{2} ( 3 x )}{x} d x

\int sin^{3} (11 x) cos^{9} (11 x) d x