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Solved example of logarithmic differentiation

Apply natural logarithm to both sides of the equality

Using the power rule of logarithms: $\log_a(x^n)=n\cdot\log_a(x)$

Derive both sides of the equality with respect to $x$

The derivative of the linear function is equal to $1$

Any expression multiplied by $1$ is equal to itself

Simplify the fraction $\frac{x}{x}$ by $x$

Substitute $y$ for the original function: $x^x$

The derivative of the function results in

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- (\sin^2(\theta))'
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