derivative of (xln(x)^2)

Lösung

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

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

Schritte zur Lösung

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

Vereinfache

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

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

Wende die Produktregel an:

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

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

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

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

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

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

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

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

\frac{\partial}{\partial x} (x^{2} + 2 x y + y^{4})

t an g e n t f (x) = \frac{4}{x}, (- 9, - \frac{4}{9})

\frac{\partial}{\partial y} (x + y - 8)

\int_{0}^{8} \frac{1}{3 x} d x

\frac{\partial}{\partial x} (e^{x^{2}} + 2 y^{3})