derivative of (ln(x)^2cos(x))

Lösung

\frac{d}{d x} ((ln (x))^{2} cos (x))

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

Schritte zur Lösung

\frac{d}{d x} ((ln (x))^{2} cos (x))

Wende die Produktregel an:

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

f = (ln (x))^{2}, g = cos (x)

= \frac{d}{d x} ((ln (x))^{2}) cos (x) + \frac{d}{d x} (cos (x)) (ln (x))^{2}

\frac{d}{d x} ((ln (x))^{2}) = \frac{2 ln ( x )}{x}

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

= \frac{2 ln ( x )}{x} cos (x) + (- sin (x)) (ln (x))^{2}

Vereinfache

\frac{2 ln ( x )}{x} cos (x) + (- sin (x)) ln^{2} (x) : \frac{2 ln ( x ) cos ( x )}{x} - ln^{2} (x) sin (x)

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

\frac{d}{d t} (e^{t^{2}})

\int \frac{( 7 x ^{2} + 2 x - 7 )}{x ^{3} - x} d x

d er i v a t i v e (7 x^{2} - 14 x + 14) e^{x}

\frac{\partial}{\partial y} (y^{2} sin (x))

y^{^{'}} = x y - 3 y