(\partial)/(\partial x)((x^2)^{-1/2})

Lösung

\frac{\partial}{\partial x} ((x^{2})^{- \frac{1}{2}})

- \frac{1}{x ^{2}}

Schritte zur Lösung

\frac{\partial}{\partial x} ((x^{2})^{- \frac{1}{2}})

Wende die Kettenregel an:

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

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

\frac{\partial}{\partial x} (x^{2}) = 2 x

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

Vereinfache

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

= - \frac{1}{x ^{2}}

d er i v a t i v e u (x) = 3 x^{2} - x + 6

d er i v a t i v e f (x) = \frac{5}{4 x}, x = 2

\frac{d ^{2}}{d x ^{2}} (3 x^{- 3} + 5 x^{2})

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

\frac{d x}{x - x ^{2}} = 3 d t