derivative of \sqrt[5]{x^2-x+7}

Lösung

\frac{d}{d x} (5 x^{2} - x + 7)

\frac{2 x - 1}{5 ( x ^{2} - x + 7 ) ^{\frac{4}{5}}}

Schritte zur Lösung

\frac{d}{d x} (5 x^{2} - x + 7)

Wende die Kettenregel an:

\frac{1}{5 ( x ^{2} - x + 7 ) ^{\frac{4}{5}}} \frac{d}{d x} (x^{2} - x + 7)

= \frac{1}{5 ( x ^{2} - x + 7 ) ^{\frac{4}{5}}} \frac{d}{d x} (x^{2} - x + 7)

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

= \frac{1}{5 ( x ^{2} - x + 7 ) ^{\frac{4}{5}}} (2 x - 1)

Vereinfache

\frac{1}{5 ( x ^{2} - x + 7 ) ^{\frac{4}{5}}} (2 x - 1) : \frac{2 x - 1}{5 ( x ^{2} - x + 7 ) ^{\frac{4}{5}}}

= \frac{2 x - 1}{5 ( x ^{2} - x + 7 ) ^{\frac{4}{5}}}

\frac{\partial}{\partial z} (2 y^{3} z)

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

\frac{\partial}{\partial y} (x^{2} - x y + y^{2} - y)

\int x^{5} (cos (x^{3})) d x

\frac{d}{d z} (ln (\frac{a ^{2} - z ^{2}}{a ^{2} + z ^{2}}))