derivative of x^2*tan(1/x)

Lösung

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

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

Schritte zur Lösung

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

Wende die Produktregel an:

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

f = x^{2}, g = tan (\frac{1}{x})

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

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

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

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

Vereinfache

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

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

x \to 0 lim (\frac{1}{cos ( 2 x )})

\int_{0}^{L} 0 d x

x \to 3 lim (\frac{x ^{2} - 1}{x + 1})

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

\frac{d y}{d x} = \frac{x}{2 y ^{2}}, y (0) = 1