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Beliebt Rechnen >

derivative of ln(xe^{-9x})

Lösung

\frac{d}{d x} (ln (x e^{- 9 x}))

Lösung

\frac{1}{x} - 9

Schritte zur Lösung

\frac{d}{d x} (ln (x e^{- 9 x}))

Vereinfache

ln (x e^{- 9 x}) : ln (x) - 9 x

= \frac{d}{d x} (ln (x) - 9 x)

Wende die Summen-/Differenzregel an:

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

= \frac{d}{d x} (ln (x)) - \frac{d}{d x} (9 x)

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

\frac{d}{d x} (9 x) = 9

= \frac{1}{x} - 9

Graph

Beliebte Beispiele

(\partial)/(\partial x)((c-b)/(a-x))

\frac{\partial}{\partial x} (\frac{c - b}{a - x})

y^'=((1+x))/(xy^{14)}

y^{^{'}} = \frac{( 1 + x )}{x y ^{14}}

tangent y=(x^2-15)^4,\at x=4

t an g e n t y = (x^{2} - 15)^{4}, at x = 4

derivative of ln(-cos(x^2+1))

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

limit as x approaches 7 of (x-7)^2+x^2

x \to 7 lim ((x - 7)^{2} + x^{2})