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

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

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(\partial)/(\partial x)(ln(x^2z^2))

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

\frac{2}{x}

Solution steps

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

Treat

z

as a constant

Apply the chain rule:

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

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

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

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

Simplify

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

= \frac{2}{x}

\int \frac{1 + x}{1 - x} d x

\int (e^{x} - 1)^{2} d x

f (x) = a^{2 x}

8 y y^{^{'}} = x

\frac{6}{x ^{5}} - \frac{2}{x}

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