derivative of sin(ln(x)+cos(ln(x)))

Lösung

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

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

Schritte zur Lösung

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

Wende die Summen-/Differenzregel an:

(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}

Wende Regel an

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

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

d er i v a t i v e f (x) = - 3 x^{3}

in v erse l a pl a ce \frac{( s + 6 )}{( s ^{2} + 6 s + 25 )}

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

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

\frac{d}{d x} (5^{x s i n (x)})