derivative y=2x^2log_{e}(x)-x^2

Lösung

ableitung von

y = 2 x^{2} lo g_{e} (x) - x^{2}

4 x ln (x)

Schritte zur Lösung

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

Vereinfache

2 x^{2} lo g_{e} (x) - x^{2} : 2 x^{2} ln (x) - x^{2}

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

Wende die Summen-/Differenzregel an:

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

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

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

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

= 2 (2 x ln (x) + x) - 2 x

Vereinfache

2 (2 x ln (x) + x) - 2 x : 4 x ln (x)

= 4 x ln (x)

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

\frac{d}{d x} (\frac{3}{4 x - 5})

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

\frac{d y}{d x} = \frac{x}{3 y ^{2}}

n = 1 \sum \infty \frac{25 n !}{n ^{n}}