derivative of x(ln(x)^2)

Lösung

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

ln^{2} (x) + 2 ln (x)

Schritte zur Lösung

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

Wende die Produktregel an:

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

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

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

\frac{d x}{d x} = 1

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

= 1 \cdot (ln (x))^{2} + \frac{2 ln ( x )}{x} x

Vereinfache

1 \cdot ln^{2} (x) + \frac{2 ln ( x )}{x} x : ln^{2} (x) + 2 ln (x)

= ln^{2} (x) + 2 ln (x)

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

h \to 0 lim (\frac{( x + h ) ^{- 5} - x ^{- 5}}{h})

y^{^{''}} + 8 y^{^{'}} + 25 y = 0

t an g e n t y = x^{3} - 2 x + 1, (2, 5)

\frac{d y}{d x} + a y = b