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Beliebt Rechnen >

derivative of y*cos(x)

Lösung

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

Lösung

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

Schritte zur Lösung

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

Wende die Produktregel an:

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

f = y, g = cos (x)

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

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

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

Vereinfache

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

Beliebte Beispiele

derivative of a(1-sin(x))

\frac{d}{d x} (a (1 - sin (x)))

derivative of 7+x^2

\frac{d}{d x} (7 + x^{2})

integral of 1/(x(x))

\int \frac{1}{x ( x )} d x

integral of 8/(x^2+4)

\int \frac{8}{x ^{2} + 4} d x

derivative of x^3sec(x)

\frac{d}{d x} (x^{3} sec (x))