derivative f(x)= x/((x-7)^2)

Lösung

ableitung von

f (x) = \frac{x}{( x - 7 ) ^{2}}

\frac{- 7 - x}{( x - 7 ) ^{3}}

Schritte zur Lösung

\frac{d}{d x} (\frac{x}{( x - 7 ) ^{2}})

Wende die Quotientenregel an:

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

= \frac{\frac{d x}{d x} ( x - 7 ) ^{2} - \frac{d}{d x} ( ( x - 7 ) ^{2} ) x}{( ( x - 7 ) ^{2} ) ^{2}}

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

\frac{d}{d x} ((x - 7)^{2}) = 2 (x - 7)

= \frac{1 \cdot ( x - 7 ) ^{2} - 2 ( x - 7 ) x}{( ( x - 7 ) ^{2} ) ^{2}}

Vereinfache

\frac{1 \cdot ( x - 7 ) ^{2} - 2 ( x - 7 ) x}{( ( x - 7 ) ^{2} ) ^{2}} : \frac{- 7 - x}{( x - 7 ) ^{3}}

= \frac{- 7 - x}{( x - 7 ) ^{3}}

f (x) = \frac{( e ^{x} + e ^{- x} )}{2}

x \to 0 lim (\frac{x}{x + ∣ x ∣})

a re a y = \frac{1}{18 x ^{2}}, y = x, y = \frac{x}{10}

\int \frac{x - 4}{x ^{2}} d x

d er i v a t i v e f (x) = 6 e^{x} (cos (x) - sin (x))