derivative of cos(xsec^7(x))

Lösung

\frac{d}{d x} (cos (x) sec^{7} (x))

6 sec^{7} (x) sin (x)

Schritte zur Lösung

\frac{d}{d x} (cos (x) sec^{7} (x))

Wende die Produktregel an:

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

f = cos (x), g = sec^{7} (x)

= \frac{d}{d x} (cos (x)) sec^{7} (x) + \frac{d}{d x} (sec^{7} (x)) cos (x)

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

\frac{d}{d x} (sec^{7} (x)) = 7 sec^{7} (x) tan (x)

= (- sin (x)) sec^{7} (x) + 7 sec^{7} (x) tan (x) cos (x)

Vereinfache

(- sin (x)) sec^{7} (x) + 7 sec^{7} (x) tan (x) cos (x) : 6 sec^{7} (x) sin (x)

= 6 sec^{7} (x) sin (x)

\int 3 sin^{3} (x co) s^{2} x d x

x \to 1 lim (\frac{2 x - 5}{x + 1})

\frac{d}{d x} (\frac{k x + a}{b x + c})

\int ln (2 x + 1) d x

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