derivative (sin(x^2))/(3x)

Lösung

ableitung von

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

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

Schritte zur Lösung

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

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

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

Wende die Quotientenregel an:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

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

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

\frac{d x}{d x} = 1

= \frac{1}{3} \cdot \frac{cos ( x ^{2} ) \cdot 2 xx - 1 \cdot sin ( x ^{2} )}{x ^{2}}

Vereinfache

\frac{1}{3} \cdot \frac{cos ( x ^{2} ) \cdot 2 xx - 1 \cdot sin ( x ^{2} )}{x ^{2}} : \frac{2 x ^{2} cos ( x ^{2} ) - sin ( x ^{2} )}{3 x ^{2}}

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

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

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y^{^{''}} - 4 y^{^{'}} + 3 y = 2 cos (3 t)

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