What is (\partial)/(\partial x)(ln(1+z)+xy^2+z) ?

The answer to (\partial)/(\partial x)(ln(1+z)+xy^2+z) is y^2

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(\partial)/(\partial x)(ln(1+z)+xy^2+z)

\frac{\partial}{\partial x} (ln (1 + z) + x y^{2} + z)

y^{2}

Solution steps

\frac{\partial}{\partial x} (ln (1 + z) + x y^{2} + z)

Treat

z, y

as constants

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (ln (1 + z)) + \frac{\partial}{\partial x} (x y^{2}) + \frac{\partial}{\partial x} (z)

\frac{\partial}{\partial x} (ln (1 + z)) = 0

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

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

= 0 + y^{2} + 0

Simplify

= y^{2}

What is (\partial)/(\partial x)(ln(1+z)+xy^2+z) ?
The answer to (\partial)/(\partial x)(ln(1+z)+xy^2+z) is y^2