derivative of xcos(xy)

Lösung

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

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

Schritte zur Lösung

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

Wende die Produktregel an:

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

f = x, g = cos (x y)

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

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

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

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

Vereinfache

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

\int_{6}^{8} \frac{1}{( x - 6 ) ^{3}} d x

t a y l or \frac{1}{1 - 2 x}

\int \frac{cos ( 2 t )}{( 1 + sin ( 2 t ) ) ^{4}} d t

y^{3} - (6 x + 6) + 3 x y^{2} y^{^{'}} = 0

x \to 0 + lim (tan^{2 x} (x))