What is (\partial)/(\partial y)(3.5yzcos(xyz)) ?

The answer to (\partial)/(\partial y)(3.5yzcos(xyz)) is 3.5z(cos(yzx)-yzxsin(yzx))

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

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

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

Solution steps

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

Treat

z, x

as constants

Take the constant out:

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

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

Apply the Product Rule:

(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)

Simplify

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

What is (\partial)/(\partial y)(3.5yzcos(xyz)) ?
The answer to (\partial)/(\partial y)(3.5yzcos(xyz)) is 3.5z(cos(yzx)-yzxsin(yzx))