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Beliebt Rechnen >

derivative of x*cos(y)

Lösung

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

Lösung

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

Schritte zur Lösung

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

Wende die Produktregel an:

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

f = x, g = cos (y)

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

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

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

= 1 \cdot cos (y) + (- sin (y) \frac{d y}{d x}) x

Vereinfache

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

Beliebte Beispiele

limit as x approaches 0 of (cot(pix)sin(x))/(2sec(x))

x \to 0 lim (\frac{cot ( π x ) sin ( x )}{2 sec ( x )})

integral of cos(3t)

\int cos (3 t) d t

derivative of 2sqrt({f)(x})

\frac{d}{d x} (2 f (x))

integral of (e^{-x^2})^2

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

integral of (x^2)/3

\int \frac{x ^{2}}{3} d x