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Beliebt Rechnen >

derivative xsin(5x)

Lösung

ableitung von

x sin (5 x)

Lösung

sin (5 x) + 5 x cos (5 x)

Schritte zur Lösung

\frac{d}{d x} (x sin (5 x))

Wende die Produktregel an:

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

f = x, g = sin (5 x)

= \frac{d x}{d x} sin (5 x) + \frac{d}{d x} (sin (5 x)) x

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

\frac{d}{d x} (sin (5 x)) = cos (5 x) \cdot 5

= 1 \cdot sin (5 x) + cos (5 x) \cdot 5 x

Vereinfache

= sin (5 x) + 5 x cos (5 x)

Graph

Beliebte Beispiele

tangent-2sin(x),\at x=-pi/3

t an g e n t - 2 sin (x), at x = - \frac{π}{3}

integral from 3 to 0 of x^2

\int_{3}^{0} x^{2} d x

tangent (5x)/(x+2)

t an g e n t \frac{5 x}{x + 2}

integral of (sin(x))^6

\int (sin (x))^{6} d x

(\partial)/(\partial x)(ze^x)

\frac{\partial}{\partial x} (z e^{x})