(\partial)/(\partial y)(3.5yzcos(xyz))

Lösung

\frac{\partial}{\partial y} (3.5 yz cos (x yz))

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

Schritte zur Lösung

\frac{\partial}{\partial y} (3.5 yz cos (x yz))

Behandle

z, x

als Konstanten

Entferne die Konstante:

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

= 3.5 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)

= 3.5 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

= 3.5 z (1 \cdot cos (x yz) + (- sin (x yz) z x) y)

Vereinfache

= 3.5 z (cos (yz x) - yz x sin (yz x))

x y^{^{'}} + 45 y = 0

\frac{d}{d t} (sin^{3} (t))

\frac{d}{d x} (x^{2} tan (2 x^{5}))

f (x) = \frac{e ^{x}}{e ^{x} + 1}

\int \frac{e ^{6 s i n (x)}}{sec ( x )} d x