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Beliebt Rechnen >

derivative y=x^2cos(4/x)

Lösung

ableitung von

y = x^{2} cos (\frac{4}{x})

Lösung

2 x cos (\frac{4}{x}) + 4 sin (\frac{4}{x})

Schritte zur Lösung

\frac{d}{d x} (x^{2} cos (\frac{4}{x}))

Wende die Produktregel an:

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

f = x^{2}, g = cos (\frac{4}{x})

= \frac{d}{d x} (x^{2}) cos (\frac{4}{x}) + \frac{d}{d x} (cos (\frac{4}{x})) x^{2}

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

\frac{d}{d x} (cos (\frac{4}{x})) = \frac{4 sin ( \frac{4}{x} )}{x ^{2}}

= 2 x cos (\frac{4}{x}) + \frac{4 sin ( \frac{4}{x} )}{x ^{2}} x^{2}

\frac{4 sin ( \frac{4}{x} )}{x ^{2}} x^{2} = 4 sin (\frac{4}{x})

= 2 x cos (\frac{4}{x}) + 4 sin (\frac{4}{x})

Graph

Beliebte Beispiele

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n or ma l f (x) = x^{4} + 2 e^{x}, (0, 2)

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x \to 0 + lim (- x + 5)

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x \to 9 - lim (\frac{x ^{9}}{x - 9})