(\partial)/(\partial x)(ln(x/4))

Solução

\frac{\partial}{\partial x} (ln (\frac{x}{4}))

\frac{1}{x}

Passos da solução

\frac{\partial}{\partial x} (ln (\frac{x}{4}))

Aplicar a regra da cadeia:

\frac{1}{\frac{x}{4}} \frac{\partial}{\partial x} (\frac{x}{4})

= \frac{1}{\frac{x}{4}} \frac{\partial}{\partial x} (\frac{x}{4})

\frac{\partial}{\partial x} (\frac{x}{4}) = \frac{1}{4}

= \frac{1}{\frac{x}{4}} \cdot \frac{1}{4}

Simplificar

\frac{1}{\frac{x}{4}} \cdot \frac{1}{4} : \frac{1}{x}

= \frac{1}{x}

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