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Beliebt Rechnen >

derivative of xsin(xy)

Lösung

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

Lösung

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

Schritte zur Lösung

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

Wende die Produktregel an:

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

f = x, g = sin (x y)

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

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

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

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

Vereinfache

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

Beliebte Beispiele

(dy}{dt}=\frac{3y)/t+t^5

\frac{d y}{d t} = \frac{3 y}{t} + t^{5}

limit as x approaches c of f(x)

x \to c lim (f (x))

derivative (x^2)/(5+4x)

d er i v a t i v e \frac{x ^{2}}{5 + 4 x}

fläche e^x,e^{-3x},ln(4)

a re a e^{x}, e^{- 3 x}, ln (4)

(dx)/(dt)=1-x^2

\frac{d x}{d t} = 1 - x^{2}