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}

\int \frac{x}{2} + \frac{2}{x} d x

\frac{\partial}{\partial x} (\frac{x + y}{x y - 1})

\frac{d y}{d x} = sin (y) + 1

\frac{d}{d x} (x^{3 c o s (x)})

f (x) = 7 x

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