derivative of sqrt(((x+1/(x+6))^8))

Lösung

\frac{d}{d x} (\frac{x + 1}{x + 6})^{8}

\frac{20 ( x + 1 ) ^{3}}{( x + 6 ) ^{5}}

Schritte zur Lösung

\frac{d}{d x} (\frac{x + 1}{x + 6})^{8}

Wende die Kettenregel an:

\frac{1}{2 ( \frac{x + 1}{x + 6} ) ^{8}} \frac{d}{d x} ((\frac{x + 1}{x + 6})^{8})

= \frac{1}{2 ( \frac{x + 1}{x + 6} ) ^{8}} \frac{d}{d x} ((\frac{x + 1}{x + 6})^{8})

\frac{d}{d x} ((\frac{x + 1}{x + 6})^{8}) = \frac{40 ( x + 1 ) ^{7}}{( x + 6 ) ^{9}}

= \frac{1}{2 ( \frac{x + 1}{x + 6} ) ^{8}} \cdot \frac{40 ( x + 1 ) ^{7}}{( x + 6 ) ^{9}}

Vereinfache

\frac{1}{2 ( \frac{x + 1}{x + 6} ) ^{8}} \cdot \frac{40 ( x + 1 ) ^{7}}{( x + 6 ) ^{9}} : \frac{20 ( x + 1 ) ^{3}}{( x + 6 ) ^{5}}

= \frac{20 ( x + 1 ) ^{3}}{( x + 6 ) ^{5}}

y^{^{'}} = \frac{1}{( t - 1 ) ( y + 1 )}

d er i v a t i v e f (x) = x^{3} (x - 6)^{2}

f (x) = x - 1 + x + 1

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

\int_{0}^{π} 14 sin^{4} (x) d x