What is (\partial)/(\partial x)(ln(x*cos(y))) ?

The answer to (\partial)/(\partial x)(ln(x*cos(y))) is 1/x

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(\partial)/(\partial x)(ln(x*cos(y)))

\frac{\partial}{\partial x} (ln (x \cdot cos (y)))

\frac{1}{x}

Solution steps

\frac{\partial}{\partial x} (ln (x cos (y)))

Treat

y

as a constant

Apply the chain rule:

\frac{1}{x cos ( y )} \frac{\partial}{\partial x} (x cos (y))

= \frac{1}{x cos ( y )} \frac{\partial}{\partial x} (x cos (y))

\frac{\partial}{\partial x} (x cos (y)) = cos (y)

= \frac{1}{x cos ( y )} cos (y)

Simplify

\frac{1}{x cos ( y )} cos (y) : \frac{1}{x}

= \frac{1}{x}

What is (\partial)/(\partial x)(ln(x*cos(y))) ?
The answer to (\partial)/(\partial x)(ln(x*cos(y))) is 1/x