What is the derivative of cos(ln(x)-sin(ln(x))) ?

The derivative of cos(ln(x)-sin(ln(x))) is (-sin(ln(x))-cos(ln(x)))/x

What is the first derivative of cos(ln(x)-sin(ln(x))) ?

The first derivative of cos(ln(x)-sin(ln(x))) is (-sin(ln(x))-cos(ln(x)))/x

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

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

Solution steps

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

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

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

\frac{d}{d x} (sin (ln (x))) = \frac{cos ( ln ( x ) )}{x}

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

Apply rule

\frac{a}{c} \pm \frac{b}{c} = \frac{a \pm b}{c}

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

\frac{d}{d y} (2 y^{3} + \frac{1}{24 y})

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

x \to 1 + lim (x^{\frac{6}{1 - x}})

\frac{d}{d x} (\frac{( x - 3 ) ( x ^{2} + 3 x + 9 )}{x ^{3}})

\frac{d}{d y} (\frac{3}{y})

What is the derivative of cos(ln(x)-sin(ln(x))) ?
The derivative of cos(ln(x)-sin(ln(x))) is (-sin(ln(x))-cos(ln(x)))/x
What is the first derivative of cos(ln(x)-sin(ln(x))) ?
The first derivative of cos(ln(x)-sin(ln(x))) is (-sin(ln(x))-cos(ln(x)))/x