derivative of 5/(cos^2(x))

Lösung

\frac{d}{d x} (\frac{5}{cos ^{2} ( x )})

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

Schritte zur Lösung

\frac{d}{d x} (\frac{5}{cos ^{2} ( x )})

Vereinfache

\frac{5}{cos ^{2} ( x )} : 5 sec^{2} (x)

= \frac{d}{d x} (5 sec^{2} (x))

Entferne die Konstante:

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

= 5 \frac{d}{d x} (sec^{2} (x))

Wende die Kettenregel an:

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

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

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

= 5 \cdot 2 sec (x) sec (x) tan (x)

Vereinfache

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

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

x \to 2 - lim (\frac{7}{x - 2})

d er i v a t i v e f (x) = 3 x^{2} + 3 x + 3

\int e^{x} (1 + e^{1 - x}) d x

x y^{^{'}} + 6 x^{2} y = x e^{5 x}

\int sec (x) tan^{2} (x) d x