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}

\int \frac{1}{( x ^{2} - 441 ) ^{\frac{3}{2}}} d x

\frac{d}{d x} (3 (3 x^{2} + 5 x - 1)^{2})

y^{^{''}} - 2 y^{^{'}} + 5 y = e^{- 2 t}

\frac{2 s - 6}{s ^{2} + 9}

\frac{d}{d x} (sin^{4} (2 x co) s^{4} 3 x)

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