derivative of 7sec(xtan(x))

Lösung

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

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

Schritte zur Lösung

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

Entferne die Konstante:

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

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

Wende die Produktregel an:

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

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

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

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

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

= 7 (sec (x) tan (x) tan (x) + sec^{2} (x) sec (x))

Vereinfache

7 (sec (x) tan (x) tan (x) + sec^{2} (x) sec (x)) : 7 (- sec (x) + 2 sec^{3} (x))

= 7 (- sec (x) + 2 sec^{3} (x))

\int_{2}^{4} e^{3 x - y} d y

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

x \to 0 lim (\frac{5 x ^{2}}{2})

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

f (x) = x^{2} cos (x)