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Beliebt Rechnen >

derivative of \sqrt[3]{x}*tan(5x)

Lösung

\frac{d}{d x} (3 x \cdot tan (5 x))

Lösung

\frac{tan ( 5 x )}{3 x ^{\frac{2}{3}}} + 5 3 x sec^{2} (5 x)

Schritte zur Lösung

\frac{d}{d x} (3 x tan (5 x))

Wende die Produktregel an:

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

f = 3 x, g = tan (5 x)

= \frac{d}{d x} (3 x) tan (5 x) + \frac{d}{d x} (tan (5 x)) 3 x

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

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

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

\frac{1}{3 x ^{\frac{2}{3}}} tan (5 x) = \frac{tan ( 5 x )}{3 x ^{\frac{2}{3}}}

= \frac{tan ( 5 x )}{3 x ^{\frac{2}{3}}} + 5 3 x sec^{2} (5 x)

Graph

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