derivative of x^2ln|x|

Lösung

\frac{d}{d x} (x^{2} ln ∣ x ∣)

2 x ln ∣ x ∣ + x

Schritte zur Lösung

\frac{d}{d x} (x^{2} ln ∣ x ∣)

Wende die Produktregel an:

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

f = x^{2}, g = ln ∣ x ∣

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

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

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

= 2 x ln ∣ x ∣ + \frac{1}{x} x^{2}

\frac{1}{x} x^{2} = x

= 2 x ln ∣ x ∣ + x

d er i v a t i v e f (x) = \frac{x ^{2} + 2 x}{( x + 1 ) ^{2}}

\frac{\partial}{\partial x} (4 e^{yz} cos (x yz))

x \to 7 lim (\frac{- 2}{7 - x})

t an g e n t y = \frac{6 x}{x + 2}, (4, 4)

\int \frac{( x - 2 )}{x ^{2} - 7 x + 12} d x