What is (\partial)/(\partial x)(xln(y)+y^2z+z^2) ?

The answer to (\partial)/(\partial x)(xln(y)+y^2z+z^2) is ln(y)

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(\partial)/(\partial x)(xln(y)+y^2z+z^2)

\frac{\partial}{\partial x} (x ln (y) + y^{2} z + z^{2})

ln (y)

Solution steps

\frac{\partial}{\partial x} (x ln (y) + y^{2} z + z^{2})

Treat

y, z

as constants

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{\partial}{\partial x} (x ln (y)) + \frac{\partial}{\partial x} (y^{2} z) + \frac{\partial}{\partial x} (z^{2})

\frac{\partial}{\partial x} (x ln (y)) = ln (y)

\frac{\partial}{\partial x} (y^{2} z) = 0

\frac{\partial}{\partial x} (z^{2}) = 0

= ln (y) + 0 + 0

Simplify

= ln (y)

What is (\partial)/(\partial x)(xln(y)+y^2z+z^2) ?
The answer to (\partial)/(\partial x)(xln(y)+y^2z+z^2) is ln(y)