derivative of (x+1/(x+3))

Lösung

\frac{d}{d x} (\frac{x + 1}{x + 3})

\frac{2}{( x + 3 ) ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{x + 1}{x + 3})

Wende die Quotientenregel an:

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

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

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

\frac{d}{d x} (x + 3) = 1

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

Vereinfache

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

= \frac{2}{( x + 3 ) ^{2}}

f (x) = \frac{4 x + 4}{3 x ^{\frac{2}{3}}}

\int_{- 1}^{4} 2 - 2 x d x

d er i v a t i v e cos^{3} (π x)

x^{2} \frac{d y}{d x} = 2 x y + y^{2}

x \to 2 lim (\frac{( 3 )}{x + 2})