(\partial)/(\partial y)(sin(y)cos(y))

Lösung

\frac{\partial}{\partial y} (sin (y) cos (y))

cos (2 y)

Schritte zur Lösung

\frac{\partial}{\partial y} (sin (y) cos (y))

Wende die Produktregel an:

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

f = sin (y), g = cos (y)

= \frac{\partial}{\partial y} (sin (y)) cos (y) + \frac{\partial}{\partial y} (cos (y)) sin (y)

\frac{\partial}{\partial y} (sin (y)) = cos (y)

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

= cos (y) cos (y) + (- sin (y)) sin (y)

Vereinfache

cos (y) cos (y) + (- sin (y)) sin (y) : cos (2 y)

= cos (2 y)

a re a y = 12 - x^{2}, y = - 3 x - 16

(e^{2 x} \cdot 2)^{^{'}}

d er i v a t i v e y (θ) = θ cos (θ)

d er i v a t i v e 6 x sin (x^{2})

a re a y = 1 - x^{2}, y = x^{2} - 1