derivative 1/(2sqrt(r)+7^{6/7)}

Lösung

ableitung von

\frac{1}{2 r + 7 ^{\frac{6}{7}}}

- \frac{1}{r ^{\frac{1}{2}} ( 2 r + 7 ^{\frac{6}{7}} ) ^{2}}

Schritte zur Lösung

\frac{d}{d r} (\frac{1}{2 r + 7 ^{\frac{6}{7}}})

Wende Exponentenregel an:

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

= \frac{d}{d r} ((2 r + 7^{\frac{6}{7}})^{- 1})

Wende die Kettenregel an:

- \frac{1}{( 2 r + 7 ^{\frac{6}{7}} ) ^{2}} \frac{d}{d r} (2 r + 7^{\frac{6}{7}})

= - \frac{1}{( 2 r + 7 ^{\frac{6}{7}} ) ^{2}} \frac{d}{d r} (2 r + 7^{\frac{6}{7}})

\frac{d}{d r} (2 r + 7^{\frac{6}{7}}) = \frac{1}{r ^{\frac{1}{2}}}

= - \frac{1}{( 2 r + 7 ^{\frac{6}{7}} ) ^{2}} \cdot \frac{1}{r ^{\frac{1}{2}}}

Vereinfache

- \frac{1}{( 2 r + 7 ^{\frac{6}{7}} ) ^{2}} \cdot \frac{1}{r ^{\frac{1}{2}}} : - \frac{1}{r ^{\frac{1}{2}} ( 2 r + 7 ^{\frac{6}{7}} ) ^{2}}

= - \frac{1}{r ^{\frac{1}{2}} ( 2 r + 7 ^{\frac{6}{7}} ) ^{2}}

\frac{d}{d x} (3 sin (1 + cos (4) x^{2}))

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t an g e n t f (x) = x^{3}, at x = 3