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Beliebt Rechnen >

derivative of (x-2^{x+1})

Lösung

\frac{d}{d x} ((x - 2)^{x + 1})

Lösung

(ln (x - 2) + \frac{x + 1}{x - 2}) (x - 2)^{x + 1}

Schritte zur Lösung

\frac{d}{d x} ((x - 2)^{x + 1})

Wende Exponentenregel an:

a^{b} = e^{b l n (a)}

(x - 2)^{x + 1} = e^{(x + 1) l n (x - 2)}

= \frac{d}{d x} (e^{(x + 1) l n (x - 2)})

Wende die Kettenregel an:

e^{(x + 1) l n (x - 2)} \frac{d}{d x} ((x + 1) ln (x - 2))

= e^{(x + 1) l n (x - 2)} \frac{d}{d x} ((x + 1) ln (x - 2))

\frac{d}{d x} ((x + 1) ln (x - 2)) = ln (x - 2) + \frac{x + 1}{x - 2}

= e^{(x + 1) l n (x - 2)} (ln (x - 2) + \frac{x + 1}{x - 2})

e^{(x + 1) l n (x - 2)} = (x - 2)^{x + 1}

= (ln (x - 2) + \frac{x + 1}{x - 2}) (x - 2)^{x + 1}

Graph

Beliebte Beispiele

(y^{- 2})^{^{'}}

(\partial)/(\partial x)(x^6y-2x^3y^2)

\frac{\partial}{\partial x} (x^{6} y - 2 x^{3} y^{2})

fläche y=x+4,y=x^2+x-12

a re a y = x + 4, y = x^{2} + x - 12

fläche 2(x+1),3(x+1),x=4

a re a 2 (x + 1), 3 (x + 1), x = 4

derivative x^3+x+3

d er i v a t i v e x^{3} + x + 3