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Beliebt Rechnen >

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

Lösung

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

Lösung

\frac{c - b}{( a - x ) ^{2}}

Schritte zur Lösung

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

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

= (c - b) \frac{\partial}{\partial x} (\frac{1}{a - x})

Wende Exponentenregel an:

\frac{1}{a} = a^{- 1}

= (c - b) \frac{\partial}{\partial x} ((a - x)^{- 1})

Wende die Kettenregel an:

- \frac{1}{( a - x ) ^{2}} \frac{\partial}{\partial x} (a - x)

= - \frac{1}{( a - x ) ^{2}} \frac{\partial}{\partial x} (a - x)

\frac{\partial}{\partial x} (a - x) = - 1

= (c - b) (- \frac{1}{( a - x ) ^{2}} (- 1))

Vereinfache

(c - b) (- \frac{1}{( a - x ) ^{2}} (- 1)) : \frac{c - b}{( a - x ) ^{2}}

= \frac{c - b}{( a - x ) ^{2}}

Beliebte Beispiele

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})

limit as x approaches 0+of ln(1/(x^4))

x \to 0 + lim (ln (\frac{1}{x ^{4}}))