derivative of (tan^3(x)/3)

Lösung

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

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

Schritte zur Lösung

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

Entferne die Konstante:

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

= \frac{1}{3} \frac{d}{d x} (tan^{3} (x))

Wende die Kettenregel an:

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

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

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

= \frac{1}{3} \cdot 3 (tan (x))^{2} sec^{2} (x)

Vereinfache

\frac{1}{3} \cdot 3 tan^{2} (x) sec^{2} (x) : tan^{2} (x) sec^{2} (x)

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

n = 1 \sum \infty \frac{2 n !}{n ^{5}}

\frac{\partial}{\partial x} (- 6 e^{- 3 x^{2} - y^{2}} x)

s l o p e (1 - 2 x) (3 x - 4), at x = 2

f (x) = 2 x^{2} - x + 9

d er i v a t i v e f (x) = 2 - \frac{2}{3} x