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Beliebt Rechnen >

derivative xcos(sqrt(x-3))

Lösung

ableitung von

x cos (x - 3)

Lösung

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

Schritte zur Lösung

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

Wende die Produktregel an:

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

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

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

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

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

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

Vereinfache

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

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

Graph

Beliebte Beispiele

derivative (4x^2-5x+9)/(3x+7)

d er i v a t i v e \frac{4 x ^{2} - 5 x + 9}{3 x + 7}

y^{^{'}} = e^{(t + y)}

integral of (x+7)e^{2x+3}

\int (x + 7) e^{2 x + 3} d x

integral from-2 to 3 of (33)/(x^4)

\int_{- 2}^{3} \frac{33}{x ^{4}} d x

integral of x^3-6x^2+x+3

\int x^{3} - 6 x^{2} + x + 3 d x