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Beliebt Rechnen >

derivative of tan(5x+1/(2x^2))

Lösung

\frac{d}{d x} (tan (5 x) + \frac{1}{2 x ^{2}})

Lösung

sec^{2} (5 x) \cdot 5 - \frac{1}{x ^{3}}

Schritte zur Lösung

\frac{d}{d x} (tan (5 x) + \frac{1}{2 x ^{2}})

Wende die Summen-/Differenzregel an:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (tan (5 x)) + \frac{d}{d x} (\frac{1}{2 x ^{2}})

\frac{d}{d x} (tan (5 x)) = sec^{2} (5 x) \cdot 5

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

= sec^{2} (5 x) \cdot 5 - \frac{1}{x ^{3}}

Graph

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