(\partial)/(\partial y)(3.25yzcos(xyz))

Lösung

\frac{\partial}{\partial y} (3.25 yz cos (x yz))

3.25 z (cos (yz x) - yz x sin (yz x))

Schritte zur Lösung

\frac{\partial}{\partial y} (3.25 yz cos (x yz))

Behandle

z, x

als Konstanten

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

= 3.25 z \frac{\partial}{\partial y} (y cos (x yz))

Wende die Produktregel an:

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

f = y, g = cos (x yz)

= 3.25 z (\frac{\partial}{\partial y} (y) cos (x yz) + \frac{\partial}{\partial y} (cos (x yz)) y)

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

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

= 3.25 z (1 \cdot cos (x yz) + (- sin (x yz) z x) y)

Vereinfache

= 3.25 z (cos (yz x) - yz x sin (yz x))

\frac{d}{d x} (x^{\frac{1}{3}} (x^{2} - 4))

l a pl a ce t r an s f or m 5 + 4 e - 2 t

\frac{\partial}{\partial x} (x^{3} y + x y^{2} + x y + x)

\frac{d}{d x} (\frac{- 200 ln ( \frac{x}{40} )}{x + 20})

\int_{0}^{15} 2 π x (15 x - x^{2}) d x