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Beliebt Rechnen >

derivative y= 1/(7x^{6/7)}

Lösung

ableitung von

y = \frac{1}{7 x ^{\frac{6}{7}}}

Lösung

- \frac{6}{49 x ^{\frac{13}{7}}}

Schritte zur Lösung

\frac{d}{d x} (\frac{1}{7 x ^{\frac{6}{7}}})

Entferne die Konstante:

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

= \frac{1}{7} \frac{d}{d x} (\frac{1}{x ^{\frac{6}{7}}})

Wende Exponentenregel an:

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

= \frac{1}{7} \frac{d}{d x} (x^{- \frac{6}{7}})

Wende die Potenzregel an:

\frac{d}{d x} (x^{a}) = a \cdot x^{a - 1}

= \frac{1}{7} (- \frac{6}{7} x^{- \frac{6}{7} - 1})

Vereinfache

\frac{1}{7} (- \frac{6}{7} x^{- \frac{6}{7} - 1}) : - \frac{6}{49 x ^{\frac{13}{7}}}

= - \frac{6}{49 x ^{\frac{13}{7}}}

Graph

Beliebte Beispiele

tangent f(x)=x^2-7,(4,9)

t an g e n t f (x) = x^{2} - 7, (4, 9)

inverselaplace ((s+1))/((s^2+4s+20))

in v erse l a pl a ce \frac{( s + 1 )}{( s ^{2} + 4 s + 20 )}

integral of-2xsqrt(1-x^2)

\int - 2 x 1 - x^{2} d x

derivative of y-1/(cos(x))=0

\frac{d}{d x} y - \frac{1}{cos ( x )} = 0

f(x)=ln(x+sqrt(1+x^2))

f (x) = ln (x + 1 + x^{2})