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

The answer to (\partial)/(\partial x)(cos(ln(x))) is -(sin(ln(x)))/x

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

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

- \frac{sin ( ln ( x ) )}{x}

Solution steps

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

Apply the chain rule:

- sin (ln (x)) \frac{\partial}{\partial x} (ln (x))

= - sin (ln (x)) \frac{\partial}{\partial x} (ln (x))

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

= - sin (ln (x)) \frac{1}{x}

Simplify

- sin (ln (x)) \frac{1}{x} : - \frac{sin ( ln ( x ) )}{x}

= - \frac{sin ( ln ( x ) )}{x}

\int 9 x e^{- 9 x} d x

f (x) = x^{2} - 3 x + 3

\frac{d}{d x} (d x)

\frac{1}{s ( s ^{2} + 8 s + 7 )}

\int \frac{1}{1 - 7 x} d x

What is (\partial)/(\partial x)(cos(ln(x))) ?
The answer to (\partial)/(\partial x)(cos(ln(x))) is -(sin(ln(x)))/x