derivative of x^2cos(1/x)

Lösung

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

2 x cos (\frac{1}{x}) + sin (\frac{1}{x})

Schritte zur Lösung

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

Wende die Produktregel an:

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

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

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

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

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

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

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

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

t^{^{'}}

\frac{\partial}{\partial x} (\frac{3 x}{4})

t an g e n t f (x) = 4 - 3 x^{2}, (- 2, - 8)

\int_{- π}^{π} cos^{2} (7 x) d x

\frac{d}{d x} (e^{20 x})