derivative of x^2sin(1/(x^2))

Lösung

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

2 x sin (\frac{1}{x ^{2}}) - \frac{2 cos ( \frac{1}{x ^{2}} )}{x}

Schritte zur Lösung

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

Wende die Produktregel an:

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

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

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

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

\frac{d}{d x} (sin (\frac{1}{x ^{2}})) = - \frac{2 cos ( \frac{1}{x ^{2}} )}{x ^{3}}

= 2 x sin (\frac{1}{x ^{2}}) + (- \frac{2 cos ( \frac{1}{x ^{2}} )}{x ^{3}}) x^{2}

Vereinfache

2 x sin (\frac{1}{x ^{2}}) + (- \frac{2 cos ( \frac{1}{x ^{2}} )}{x ^{3}}) x^{2} : 2 x sin (\frac{1}{x ^{2}}) - \frac{2 cos ( \frac{1}{x ^{2}} )}{x}

= 2 x sin (\frac{1}{x ^{2}}) - \frac{2 cos ( \frac{1}{x ^{2}} )}{x}

x \to 0 lim (\frac{9}{x})

\frac{d y}{d x} = - \frac{1 + x + y}{1 + x}

y^{^{''}} - 2 y^{^{'}} + 5 y = 0, y (\frac{π}{2}) = 0

\int 4 + x d x

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