d/(dp)(((10p^{0.25}+1))/(p^{0.25)})

Lösung

\frac{d}{d p} (\frac{( 10 p ^{0.25} + 1 )}{p ^{0.25}})

- \frac{0.25}{p ^{1.25}}

Schritte zur Lösung

\frac{d}{d p} (\frac{( 10 p ^{0.25} + 1 )}{p ^{0.25}})

Wende die Quotientenregel an:

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

= \frac{\frac{d}{d p} ( 10 p ^{0.25} + 1 ) p ^{0.25} - \frac{d}{d p} ( p ^{0.25} ) ( 10 p ^{0.25} + 1 )}{( p ^{0.25} ) ^{2}}

\frac{d}{d p} (10 p^{0.25} + 1) = \frac{2.5}{p ^{0.75}}

\frac{d}{d p} (p^{0.25}) = \frac{0.25}{p ^{0.75}}

= \frac{\frac{2.5}{p ^{0.75}} p ^{0.25} - \frac{0.25}{p ^{0.75}} ( 10 p ^{0.25} + 1 )}{( p ^{0.25} ) ^{2}}

Vereinfache

\frac{\frac{2.5}{p ^{0.75}} p ^{0.25} - \frac{0.25}{p ^{0.75}} ( 10 p ^{0.25} + 1 )}{( p ^{0.25} ) ^{2}} : - \frac{0.25}{p ^{1.25}}

= - \frac{0.25}{p ^{1.25}}

\int_{2}^{4} x^{2} \frac{( 2 x - 3 )}{6} d x

x \to 2 + lim (a x^{2} - b x + 3)

\int_{0}^{2} \int_{0}^{1} x y e^{x y^{2}} d y d x

\int \frac{1}{x ^{2} + 11} d x

\frac{d P}{d t} = (\frac{P}{5}) (lo g_{e} (\frac{3000}{P}))