derivative of-3/(sqrt(x^5))

Lösung

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

\frac{15}{2 x ^{\frac{7}{2}}}

Schritte zur Lösung

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

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

= - 3 \frac{d}{d x} (\frac{1}{x ^{5}})

Wende Exponentenregel an:

\frac{1}{a} = a^{- 1}

= - 3 \frac{d}{d x} ((x^{5})^{- \frac{1}{2}})

Wende die Kettenregel an:

- \frac{1}{2 ( x ^{5} ) ^{\frac{3}{2}}} \frac{d}{d x} (x^{5})

= - \frac{1}{2 ( x ^{5} ) ^{\frac{3}{2}}} \frac{d}{d x} (x^{5})

\frac{d}{d x} (x^{5}) = 5 x^{4}

= - 3 (- \frac{1}{2 ( x ^{5} ) ^{\frac{3}{2}}} \cdot 5 x^{4})

Vereinfache

- 3 (- \frac{1}{2 ( x ^{5} ) ^{\frac{3}{2}}} \cdot 5 x^{4}) : \frac{15}{2 x ^{\frac{7}{2}}}

= \frac{15}{2 x ^{\frac{7}{2}}}

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

x \to 0 lim (\frac{x}{x ^{2} - 9 x})

x^{2} y^{^{'}} + 2 x y = ln (x), y (1) = 3

\int \frac{( 2 e ^{x} )}{x} d x

\frac{d}{d x} (cos (2 x) - 2 sin (x))