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Beliebt Rechnen >

derivative y=x^{1-x}

Lösung

ableitung von

y = x^{1 - x}

Lösung

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

Schritte zur Lösung

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

Wende Exponentenregel an:

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

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

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

Wende die Kettenregel an:

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

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

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

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

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

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

Graph

Beliebte Beispiele

tangent f(x)= 1/((1+x^2))

t an g e n t f (x) = \frac{1}{( 1 + x ^{2} )}

derivative of 4-(20/(x^3)+3/(x^5))

\frac{d}{d x} (4 - \frac{20}{x ^{3}} + \frac{3}{x ^{5}})

tangent f(x)=x^2+x,\at (x=1)

t an g e n t f (x) = x^{2} + x, at (x = 1)

(\partial)/(\partial x)(y^2+x^2)

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

3xy^2y^'=3x^4+y^3

3 x y^{2} y^{^{'}} = 3 x^{4} + y^{3}