derivative sin(x)ln(cos(x))

Lösung

ableitung von

sin (x) ln (cos (x))

cos (x) ln (cos (x)) - tan (x) sin (x)

Schritte zur Lösung

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

Wende die Produktregel an:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = sin (x), g = ln (cos (x))

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

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

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

= cos (x) ln (cos (x)) + (- tan (x)) sin (x)

Vereinfache

= cos (x) ln (cos (x)) - tan (x) sin (x)

x \to - 1 lim (3 x^{2} + \frac{4}{x ^{2}})

\int - 9 cot (x) ln (sin (x)) d x

\frac{d}{d x} (4 e^{3 x^{2}} sin (cos (2 x)))

\frac{d}{d x} (sin^{2} (x) - cos (x))

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