derivative of ((x^2+7/(x^2-7))^3)

Lösung

\frac{d}{d x} ((\frac{x ^{2} + 7}{x ^{2} - 7})^{3})

- \frac{84 x ( x ^{2} + 7 ) ^{2}}{( x ^{2} - 7 ) ^{4}}

Schritte zur Lösung

\frac{d}{d x} ((\frac{x ^{2} + 7}{x ^{2} - 7})^{3})

Wende die Kettenregel an:

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

= 3 (\frac{x ^{2} + 7}{x ^{2} - 7})^{2} \frac{d}{d x} (\frac{x ^{2} + 7}{x ^{2} - 7})

\frac{d}{d x} (\frac{x ^{2} + 7}{x ^{2} - 7}) = - \frac{28 x}{( x ^{2} - 7 ) ^{2}}

= 3 (\frac{x ^{2} + 7}{x ^{2} - 7})^{2} (- \frac{28 x}{( x ^{2} - 7 ) ^{2}})

Vereinfache

3 (\frac{x ^{2} + 7}{x ^{2} - 7})^{2} (- \frac{28 x}{( x ^{2} - 7 ) ^{2}}) : - \frac{84 x ( x ^{2} + 7 ) ^{2}}{( x ^{2} - 7 ) ^{4}}

= - \frac{84 x ( x ^{2} + 7 ) ^{2}}{( x ^{2} - 7 ) ^{4}}

im pl i c i t \frac{d y}{d x}, x + y = 5

\frac{\partial}{\partial x} (\frac{x}{2})

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

\int_{0}^{\frac{π}{4}} 5 cos^{5} (2 x) d x

\frac{\partial}{\partial x} (\frac{x y}{x + y + z})