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

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

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

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

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

Solution steps

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

Treat

y, x

as constants

Take the constant out:

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

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

Apply the Product Rule:

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

f = z, g = cos (x yz)

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

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

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

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

Simplify

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

\int \frac{1}{x ^{3} 9 x ^{2} - 1} d x

\frac{d}{d x} (\frac{x ^{2}}{30})

\frac{d}{d x} (x y + x cos (x))

\int x^{2} + x d x

2 y^{^{''}} + 3 y^{^{'}} - 4 y = 5 e^{3 x}

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