What is (\partial)/(\partial x)(yln(xz^2)) ?

The answer to (\partial)/(\partial x)(yln(xz^2)) is y/x

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(\partial)/(\partial x)(yln(xz^2))

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

\frac{y}{x}

Solution steps

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

Treat

y, z

as constants

Take the constant out:

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

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

Apply the chain rule:

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

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

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

= y \frac{1}{x z ^{2}} z^{2}

Simplify

y \frac{1}{x z ^{2}} z^{2} : \frac{y}{x}

= \frac{y}{x}

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What is (\partial)/(\partial x)(yln(xz^2)) ?
The answer to (\partial)/(\partial x)(yln(xz^2)) is y/x