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

Lösung

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

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

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

\int_{12}^{13} x x^{2} - 144 d x

\frac{\partial}{\partial x} (x y - ln (x y))

\frac{d}{d x} (\frac{( 6 x ^{2} + 4 )}{( 3 y ^{2} - 4 )})

\int_{- 3}^{0} 1 + 9 - x^{2} d x

in v erse l a pl a ce \frac{200}{( s + 10 ) ( s + 100 )}