What is (\partial)/(\partial x)(xsin(xyz)) ?

The answer to (\partial)/(\partial x)(xsin(xyz)) is sin(xyz)+xyzcos(xyz)

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(\partial)/(\partial x)(xsin(xyz))

\frac{\partial}{\partial x} (x sin (x yz))

sin (x yz) + x yz cos (x yz)

Solution steps

\frac{\partial}{\partial x} (x sin (x yz))

Treat

y, z

as constants

Apply the Product Rule:

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

f = x, g = sin (x yz)

= \frac{\partial}{\partial x} (x) sin (x yz) + \frac{\partial}{\partial x} (sin (x yz)) x

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

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

= 1 \cdot sin (x yz) + cos (x yz) yz x

Simplify

= sin (x yz) + x yz cos (x yz)

\int ln (e)

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y^{^{''}} - y = t - 4 e^{- t}

\int 8 sec^{3} (2 x) d x

What is (\partial)/(\partial x)(xsin(xyz)) ?
The answer to (\partial)/(\partial x)(xsin(xyz)) is sin(xyz)+xyzcos(xyz)