derivative of ((x-6/(x+7))^3)

Lösung

\frac{d}{d x} ((\frac{x - 6}{x + 7})^{3})

\frac{39 ( x - 6 ) ^{2}}{( x + 7 ) ^{4}}

Schritte zur Lösung

\frac{d}{d x} ((\frac{x - 6}{x + 7})^{3})

Wende die Kettenregel an:

3 (\frac{x - 6}{x + 7})^{2} \frac{d}{d x} (\frac{x - 6}{x + 7})

= 3 (\frac{x - 6}{x + 7})^{2} \frac{d}{d x} (\frac{x - 6}{x + 7})

\frac{d}{d x} (\frac{x - 6}{x + 7}) = \frac{13}{( x + 7 ) ^{2}}

= 3 (\frac{x - 6}{x + 7})^{2} \frac{13}{( x + 7 ) ^{2}}

Vereinfache

3 (\frac{x - 6}{x + 7})^{2} \frac{13}{( x + 7 ) ^{2}} : \frac{39 ( x - 6 ) ^{2}}{( x + 7 ) ^{4}}

= \frac{39 ( x - 6 ) ^{2}}{( x + 7 ) ^{4}}

h \to + 0 lim (\frac{( 2 + h ) - 2}{h})

n = 0 \sum \infty \frac{n ^{2}}{n + 1}

l a pl a ce t r an s f or m x \cdot sin (A x)

\frac{d}{d x} (- 2 x^{3} + 10 - 3 x^{2} + 12 x)

in v erse l a pl a ce \frac{1}{( s ^{4} - 9 )}