derivative of x^{12}ln(x)

Lösung

\frac{d}{d x} (x^{12} ln (x))

12 x^{11} ln (x) + x^{11}

Schritte zur Lösung

\frac{d}{d x} (x^{12} ln (x))

Wende die Produktregel an:

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

f = x^{12}, g = ln (x)

= \frac{d}{d x} (x^{12}) ln (x) + \frac{d}{d x} (ln (x)) x^{12}

\frac{d}{d x} (x^{12}) = 12 x^{11}

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

= 12 x^{11} ln (x) + \frac{1}{x} x^{12}

\frac{1}{x} x^{12} = x^{11}

= 12 x^{11} ln (x) + x^{11}

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

\int \frac{( x + 16 )}{( x ^{2} + 2 x - 8 )} d x

\frac{\partial}{\partial α} (K (α) (α)^{α} L^{1 - α})

t an g e n t y = 11 x^{2}, (- 2, 44)

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