derivative of ((3x-1/(5x+2))^4)

Lösung

\frac{d}{d x} ((\frac{3 x - 1}{5 x + 2})^{4})

\frac{44 ( 3 x - 1 ) ^{3}}{( 5 x + 2 ) ^{5}}

Schritte zur Lösung

\frac{d}{d x} ((\frac{3 x - 1}{5 x + 2})^{4})

Wende die Kettenregel an:

4 (\frac{3 x - 1}{5 x + 2})^{3} \frac{d}{d x} (\frac{3 x - 1}{5 x + 2})

= 4 (\frac{3 x - 1}{5 x + 2})^{3} \frac{d}{d x} (\frac{3 x - 1}{5 x + 2})

\frac{d}{d x} (\frac{3 x - 1}{5 x + 2}) = \frac{11}{( 5 x + 2 ) ^{2}}

= 4 (\frac{3 x - 1}{5 x + 2})^{3} \frac{11}{( 5 x + 2 ) ^{2}}

Vereinfache

4 (\frac{3 x - 1}{5 x + 2})^{3} \frac{11}{( 5 x + 2 ) ^{2}} : \frac{44 ( 3 x - 1 ) ^{3}}{( 5 x + 2 ) ^{5}}

= \frac{44 ( 3 x - 1 ) ^{3}}{( 5 x + 2 ) ^{5}}

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

\int (- 7 - 7 tan^{2} (x)) d x

x \frac{d y}{d x} - 3 y = y^{2}, y (1) = 3

\int \frac{- y}{x ^{2} + y ^{2}} d x

t an g e n t f (x) = 3 x^{\frac{2}{3}} - 3, at x = 27