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

The answer to (\partial)/(\partial y)(3.5xycos(xyz)) is 3.5x(cos(xyz)-xyzsin(xyz))

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

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

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

Solution steps

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

Treat

x, z

as constants

Take the constant out:

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

= 3.5 x \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 x (\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) x z

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

Simplify

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

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What is (\partial)/(\partial y)(3.5xycos(xyz)) ?
The answer to (\partial)/(\partial y)(3.5xycos(xyz)) is 3.5x(cos(xyz)-xyzsin(xyz))