(\partial)/(\partial y)(ycos(xln(y)))

Lösung

\frac{\partial}{\partial y} (y cos (x ln (y)))

cos (x ln (y)) - x sin (x ln (y))

Schritte zur Lösung

\frac{\partial}{\partial y} (y cos (x ln (y)))

Behandle

x

als Konstante

Wende die Produktregel an:

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

f = y, g = cos (x ln (y))

= \frac{\partial}{\partial y} (y) cos (x ln (y)) + \frac{\partial}{\partial y} (cos (x ln (y))) y

\frac{\partial}{\partial y} (y) = 1

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

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

Vereinfache

1 \cdot cos (x ln (y)) + (- \frac{x sin ( x ln ( y ) )}{y}) y : cos (x ln (y)) - x sin (x ln (y))

= cos (x ln (y)) - x sin (x ln (y))

\int_{0}^{2} 1 + 3 x^{2} d x

t an g e n t 6 x^{- 3}, at x = 5

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

\int_{0}^{1} 2 x^{2} - 1 d x

\frac{d x}{d t} = 2 x (5 - x)