derivative of sqrt(x)ln(9x)

Lösung

\frac{d}{d x} (x ln (9 x))

\frac{ln ( 9 x )}{2 x} + \frac{1}{x}

Schritte zur Lösung

\frac{d}{d x} (x ln (9 x))

Wende die Produktregel an:

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

f = x, g = ln (9 x)

= \frac{d}{d x} (x) ln (9 x) + \frac{d}{d x} (ln (9 x)) x

\frac{d}{d x} (x) = \frac{1}{2 x}

\frac{d}{d x} (ln (9 x)) = \frac{1}{x}

= \frac{1}{2 x} ln (9 x) + \frac{1}{x} x

Vereinfache

\frac{1}{2 x} ln (9 x) + \frac{1}{x} x : \frac{ln ( 9 x )}{2 x} + \frac{1}{x}

= \frac{ln ( 9 x )}{2 x} + \frac{1}{x}

x \to \infty lim (- (x)^{2})

\int \frac{1}{( 1 - x )} d x

y^{^{'}} = sin (x)

x \to 1 lim (2 x^{2})

a re a f (x) = \frac{( 2 - x ^{2} )}{2}, [- \frac{5}{4}, \frac{5}{4}]