derivative f(x)=(x/7+7/x)^7

Lösung

ableitung von

f (x) = (\frac{x}{7} + \frac{7}{x})^{7}

(\frac{x}{7} + \frac{7}{x})^{6} - \frac{( x ^{2} + 49 ) ^{6}}{2401 x ^{8}}

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

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

= 7 (\frac{x}{7} + \frac{7}{x})^{6} (\frac{1}{7} - \frac{7}{x ^{2}})

Vereinfache

7 (\frac{x}{7} + \frac{7}{x})^{6} (\frac{1}{7} - \frac{7}{x ^{2}}) : (\frac{x}{7} + \frac{7}{x})^{6} - \frac{( x ^{2} + 49 ) ^{6}}{2401 x ^{8}}

= (\frac{x}{7} + \frac{7}{x})^{6} - \frac{( x ^{2} + 49 ) ^{6}}{2401 x ^{8}}

\frac{d ^{4}}{d x ^{4}} (ln (1 - x))

\int_{1}^{2} \frac{5}{8 x ^{6}} d x

n = 2 \sum \infty \frac{1}{n - 1}

x y^{^{'}} + y = 3 x + 5 x

a re a y = - 0, 7248 x 2 - 0, 2682 x + 0, 6271