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Beliebt Rechnen >

derivative of x/((x-8^2))

Lösung

\frac{d}{d x} (\frac{x}{( x - 8 ) ^{2}})

Lösung

\frac{- 8 - x}{( x - 8 ) ^{3}}

Schritte zur Lösung

\frac{d}{d x} (\frac{x}{( x - 8 ) ^{2}})

Wende die Quotientenregel an:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

= \frac{\frac{d x}{d x} ( x - 8 ) ^{2} - \frac{d}{d x} ( ( x - 8 ) ^{2} ) x}{( ( x - 8 ) ^{2} ) ^{2}}

\frac{d x}{d x} = 1

\frac{d}{d x} ((x - 8)^{2}) = 2 (x - 8)

= \frac{1 \cdot ( x - 8 ) ^{2} - 2 ( x - 8 ) x}{( ( x - 8 ) ^{2} ) ^{2}}

Vereinfache

\frac{1 \cdot ( x - 8 ) ^{2} - 2 ( x - 8 ) x}{( ( x - 8 ) ^{2} ) ^{2}} : \frac{- 8 - x}{( x - 8 ) ^{3}}

= \frac{- 8 - x}{( x - 8 ) ^{3}}

Graph

Beliebte Beispiele

tangent f(x)=e^x,\at x=ln(12)

t an g e n t f (x) = e^{x}, at x = ln (12)

limit as x approaches 1 of x^3-x^2+4x

x \to 1 lim (x^{3} - x^{2} + 4 x)

derivative sin(2x+3)

d er i v a t i v e sin (2 x + 3)

derivative of (8x+5^2)

\frac{d}{d x} ((8 x + 5)^{2})

tangent y=5x-2x^2,(-2,-18)

t an g e n t y = 5 x - 2 x^{2}, (- 2, - 18)