derivative of (1+7/x ^5)

Lösung

\frac{d}{d x} ((1 + \frac{7}{x})^{5})

- \frac{35 ( x + 7 ) ^{4}}{x ^{6}}

Schritte zur Lösung

\frac{d}{d x} ((1 + \frac{7}{x})^{5})

Wende die Kettenregel an:

5 (1 + \frac{7}{x})^{4} \frac{d}{d x} (1 + \frac{7}{x})

= 5 (1 + \frac{7}{x})^{4} \frac{d}{d x} (1 + \frac{7}{x})

\frac{d}{d x} (1 + \frac{7}{x}) = - \frac{7}{x ^{2}}

= 5 (1 + \frac{7}{x})^{4} (- \frac{7}{x ^{2}})

Vereinfache

5 (1 + \frac{7}{x})^{4} (- \frac{7}{x ^{2}}) : - \frac{35 ( x + 7 ) ^{4}}{x ^{6}}

= - \frac{35 ( x + 7 ) ^{4}}{x ^{6}}

x \to - 3 lim (5 x^{2} + 2 x)

\int \frac{1 + x}{1 - 3 x} d x

x \to 3 lim (\frac{x - 2}{x - 3})

\int \frac{3}{4 ( 4 - 3 x ) ^{7}} d x

4 y^{^{''}} + 9 y = 0