derivative of sin(\sqrt[3]{x}cos(\sqrt[3]{x}))

Lösung

\frac{d}{d x} (sin (3 x) cos (3 x))

\frac{cos ( 2 3 x )}{3 x ^{\frac{2}{3}}}

Schritte zur Lösung

\frac{d}{d x} (sin (3 x) cos (3 x))

Wende die Produktregel an:

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

f = sin (3 x), g = cos (3 x)

= \frac{d}{d x} (sin (3 x)) cos (3 x) + \frac{d}{d x} (cos (3 x)) sin (3 x)

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

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

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

Vereinfache

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

= \frac{cos ( 2 3 x )}{3 x ^{\frac{2}{3}}}

\int_{1}^{4} 1 + 9 x d x

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y^{^{''}} + 4 y = x^{2} sin (2 x)

\int (e^{- x} + e^{x})^{2} d x

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