derivative of x/((x-3^2))

Lösung

\frac{d}{d x} (\frac{x}{( x - 3 ) ^{2}})

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

Schritte zur Lösung

\frac{d}{d x} (\frac{x}{( x - 3 ) ^{2}})

Wende die Quotientenregel an:

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

= \frac{\frac{d x}{d x} ( x - 3 ) ^{2} - \frac{d}{d x} ( ( x - 3 ) ^{2} ) x}{( ( x - 3 ) ^{2} ) ^{2}}

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

\frac{d}{d x} ((x - 3)^{2}) = 2 (x - 3)

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

Vereinfache

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

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

y^{^{''}} - 4 y^{^{'}} + 5 y = e^{2 x}

\frac{\partial}{\partial x} ((1 + x y) e^{x y})

y^{^{'}} = 1 - x + y - x y

n = 1 \sum \infty \frac{4 ^{n}}{n + 1}

d er i v a t i v e f (x) = 4 x^{4} - 3 x^{\frac{5}{2}} + 2