derivative of x^2e^{-x}+(ln(x)^2)

Lösung

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

2 e^{- x} x - e^{- x} x^{2} + \frac{2 ln ( x )}{x}

Schritte zur Lösung

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

Wende die Summen-/Differenzregel an:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

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

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

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

\int_{0}^{\frac{1}{2}} x ln (2 x) d x

\frac{d}{d x} (14 x^{\frac{1}{7}})

n = 0 \sum \infty \frac{( 3 x - 2 ) ^{n}}{n}

y^{^{''}} - 4 y = (x^{2} - 5) sin (2 x)

n = 1 \sum \infty - \frac{5}{n}