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Beliebt Rechnen >

derivative of 1/(\sqrt[5]{x^2})

Lösung

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

Lösung

- \frac{2}{5 x ^{\frac{7}{5}}}

Schritte zur Lösung

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

Wende Exponentenregel an:

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

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

Wende die Kettenregel an:

- \frac{1}{5 ( x ^{2} ) ^{\frac{6}{5}}} \frac{d}{d x} (x^{2})

= - \frac{1}{5 ( x ^{2} ) ^{\frac{6}{5}}} \frac{d}{d x} (x^{2})

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

= - \frac{1}{5 ( x ^{2} ) ^{\frac{6}{5}}} \cdot 2 x

Vereinfache

- \frac{1}{5 ( x ^{2} ) ^{\frac{6}{5}}} \cdot 2 x : - \frac{2}{5 x ^{\frac{7}{5}}}

= - \frac{2}{5 x ^{\frac{7}{5}}}

Graph

Beliebte Beispiele

laplacetransform {cos(t)}

l a pl a ce t r an s f or m {cos (t)}

f (t) = cos (8 t)

derivative f(x)=x^3-3x+4

d er i v a t i v e f (x) = x^{3} - 3 x + 4

y^{''}+6y^'+5y=2x

y^{^{''}} + 6 y^{^{'}} + 5 y = 2 x

tangent f(x)=3x^{1/2}+x^{3/2},\at x=16

t an g e n t f (x) = 3 x^{\frac{1}{2}} + x^{\frac{3}{2}}, at x = 16