derivative of 1/3 tan^3(1/x)

Lösung

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

- \frac{sec ^{2} ( \frac{1}{x} ) tan ^{2} ( \frac{1}{x} )}{x ^{2}}

Schritte zur Lösung

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

Entferne die Konstante:

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

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

Wende die Kettenregel an:

3 (tan (\frac{1}{x}))^{2} \frac{d}{d x} (tan (\frac{1}{x}))

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

\frac{d}{d x} (tan (\frac{1}{x})) = - \frac{sec ^{2} ( \frac{1}{x} )}{x ^{2}}

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

Vereinfache

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

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

(x^{2} - x) y^{^{'}} = y - 2 x y

d er i v a t i v e cos^{4} (θ + 5)

n = 1 \sum \infty \frac{n}{n ^{3} + 1}

d er i v a t i v e (2 x + 3)^{5} + 10 x (2 x + 3)^{4}

s l o p e y = \frac{36 x}{x ^{2} + 36}, (- 3, - \frac{12}{5})