derivative of (4x^2+1^{-50})

Lösung

\frac{d}{d x} ((4 x^{2} + 1)^{- 50})

- \frac{400 x}{( 4 x ^{2} + 1 ) ^{51}}

Schritte zur Lösung

\frac{d}{d x} ((4 x^{2} + 1)^{- 50})

Wende die Kettenregel an:

- \frac{50}{( 4 x ^{2} + 1 ) ^{51}} \frac{d}{d x} (4 x^{2} + 1)

= - \frac{50}{( 4 x ^{2} + 1 ) ^{51}} \frac{d}{d x} (4 x^{2} + 1)

\frac{d}{d x} (4 x^{2} + 1) = 8 x

= - \frac{50}{( 4 x ^{2} + 1 ) ^{51}} \cdot 8 x

Vereinfache

- \frac{50}{( 4 x ^{2} + 1 ) ^{51}} \cdot 8 x : - \frac{400 x}{( 4 x ^{2} + 1 ) ^{51}}

= - \frac{400 x}{( 4 x ^{2} + 1 ) ^{51}}

\int (\frac{x ^{2} + 3 x - 5}{x - 3}) d x

\int 2 + x^{2} d x

\frac{d}{d x} (\frac{y}{3 x})

\frac{d y}{d x} = - 2 y, y (0) = 3

\frac{d}{d x} ((3 x^{2} + ln (x)) \cdot (5 x^{3})^{x})