What is (\partial)/(\partial x)(tan(ln(x-y))) ?

The answer to (\partial)/(\partial x)(tan(ln(x-y))) is (sec^2(ln(x-y)))/(x-y)

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(\partial)/(\partial x)(tan(ln(x-y)))

\frac{\partial}{\partial x} (tan (ln (x - y)))

\frac{sec ^{2} ( ln ( x - y ) )}{x - y}

Solution steps

\frac{\partial}{\partial x} (tan (ln (x - y)))

Treat

y

as a constant

Apply the chain rule:

sec^{2} (ln (x - y)) \frac{\partial}{\partial x} (ln (x - y))

= sec^{2} (ln (x - y)) \frac{\partial}{\partial x} (ln (x - y))

\frac{\partial}{\partial x} (ln (x - y)) = \frac{1}{x - y}

= sec^{2} (ln (x - y)) \frac{1}{x - y}

Simplify

sec^{2} (ln (x - y)) \frac{1}{x - y} : \frac{sec ^{2} ( ln ( x - y ) )}{x - y}

= \frac{sec ^{2} ( ln ( x - y ) )}{x - y}

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What is (\partial)/(\partial x)(tan(ln(x-y))) ?
The answer to (\partial)/(\partial x)(tan(ln(x-y))) is (sec^2(ln(x-y)))/(x-y)