derivative of x/((x^2+1^{1/2)})

Lösung

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

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

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

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

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

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

Vereinfache

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

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

\frac{d ^{2}}{d x ^{2}} ((2 x^{2} + 7)^{5})

\frac{d}{d x} (I n, x^{2})

\frac{d P}{d t} = k P

f (x) = 4 tan (x)

x \to 0 + lim (7 sin (x) ln (x))