derivative of 2tan(x+2tan^3(x))

Lösung

\frac{d}{d x} (2 tan (x) + 2 tan^{3} (x))

2 sec^{2} (x) (1 + 3 tan^{2} (x))

Schritte zur Lösung

\frac{d}{d x} (2 tan (x) + 2 tan^{3} (x))

Vereinfache

2 tan (x) + 2 tan^{3} (x) : 2 sec^{3} (x) sin (x)

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

Entferne die Konstante:

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

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

Wende die Produktregel an:

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

f = sec^{3} (x), g = sin (x)

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

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

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

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

Vereinfache

2 (3 sec^{3} (x) tan (x) sin (x) + cos (x) sec^{3} (x)) : 2 sec^{2} (x) (1 + 3 tan^{2} (x))

= 2 sec^{2} (x) (1 + 3 tan^{2} (x))

in v erse l a pl a ce \frac{4 s - 1}{s ^{2} ( s + 1 ) ^{3}}

x \to + 5 lim (\frac{x + 1}{x - 5})

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

\int \frac{1}{( 4 x + 1 ) ^{3}} d x

y \cdot \frac{d y}{d x} - x = 5 y^{2}