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Beliebt Rechnen >

derivative of x*sin(y)

Lösung

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

Lösung

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

Schritte zur Lösung

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

Wende die Produktregel an:

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

f = x, g = sin (y)

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

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

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

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

Vereinfache

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

Beliebte Beispiele

derivative 9xcos(x^2)

d er i v a t i v e 9 x cos (x^{2})

limit as x approaches-infinity of 6^x

x \to - \infty lim (6^{x})

y^{^{'}} - 3 y = e^{x}

derivative of (x^2(sqrt(x)))

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

tangent f(x)=4-x^2,\at x=2

t an g e n t f (x) = 4 - x^{2}, at x = 2