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

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

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

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

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

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}

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

Simplify

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

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

\frac{d}{d x} (cos (e^{3 x^{2}}))

\int (1 + x)^{4} d x

\int - 2 x^{2} d x

\int_{\frac{7}{6}}^{6} \frac{1}{1 - x ^{2}} d x

9 x^{2} cos (x) cot (x)

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