derivative of 5tan(xsec(x))

Lösung

\frac{d}{d x} (5 tan (x) sec (x))

5 (- sec (x) + 2 sec^{3} (x))

Schritte zur Lösung

\frac{d}{d x} (5 tan (x) sec (x))

Entferne die Konstante:

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

= 5 \frac{d}{d x} (tan (x) sec (x))

Wende die Produktregel an:

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

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

= 5 (\frac{d}{d x} (tan (x)) sec (x) + \frac{d}{d x} (sec (x)) tan (x))

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

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

= 5 (sec^{2} (x) sec (x) + sec (x) tan (x) tan (x))

Vereinfache

5 (sec^{2} (x) sec (x) + sec (x) tan (x) tan (x)) : 5 (- sec (x) + 2 sec^{3} (x))

= 5 (- sec (x) + 2 sec^{3} (x))

x \to 9 lim (\frac{( x ^{2} - 4 x - 45 )}{x ^{2} - 81})

\int - 2 cos (t) sin^{2} (t) d t

\frac{d}{d x} (12 x^{2} + 4)

s l o p e in t erce pt (- 1, - 2), (- 2, 3)

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