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Beliebt Rechnen >

derivative of ycos(xy)

Lösung

\frac{d}{d x} (y cos (x y))

Lösung

cos (x y) \frac{d y}{d x} - sin (x y) (y + x \frac{d y}{d x}) y

Schritte zur Lösung

\frac{d}{d x} (y cos (x y))

Wende die Produktregel an:

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

f = y, g = cos (x y)

= \frac{d y}{d x} cos (x y) + \frac{d}{d x} (cos (x y)) y

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

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

Vereinfache

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

Beliebte Beispiele

fläche 5x^2,x^2+4

a re a 5 x^{2}, x^{2} + 4

x^{2} y^{^{'}} + x y = 8

(\partial)/(\partial x)(4xy+3)

\frac{\partial}{\partial x} (4 x y + 3)

integral of xcos((pix)/2)

\int x cos (\frac{π x}{2}) d x

integral from 1 to 2 of 1/(2x+1)

\int_{1}^{2} \frac{1}{2 x + 1} d x