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

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

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

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

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

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

Solution steps

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

Apply the Sum/Difference Rule:

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

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

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

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

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

Apply rule

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

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

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

\frac{( s + 6 )}{( s ^{2} + 6 s + 25 )}

\frac{d}{d x} (x + \frac{4}{x})

\int (x + 1)^{2} ln (x + 1) d x

y^{^{'}} = y^{4}

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