derivative of ((x^2/8+x-1/x)^4)

Lösung

\frac{d}{d x} ((\frac{x ^{2}}{8} + x - \frac{1}{x})^{4})

x (\frac{x ^{2}}{8} + x - \frac{1}{x})^{3} + 4 (\frac{x ^{2}}{8} + x - \frac{1}{x})^{3} + \frac{( x ^{3} + 8 x ^{2} - 8 ) ^{3}}{128 x ^{5}}

Schritte zur Lösung

\frac{d}{d x} ((\frac{x ^{2}}{8} + x - \frac{1}{x})^{4})

Wende die Kettenregel an:

4 (\frac{x ^{2}}{8} + x - \frac{1}{x})^{3} \frac{d}{d x} (\frac{x ^{2}}{8} + x - \frac{1}{x})

= 4 (\frac{x ^{2}}{8} + x - \frac{1}{x})^{3} \frac{d}{d x} (\frac{x ^{2}}{8} + x - \frac{1}{x})

\frac{d}{d x} (\frac{x ^{2}}{8} + x - \frac{1}{x}) = \frac{x}{4} + 1 + \frac{1}{x ^{2}}

= 4 (\frac{x ^{2}}{8} + x - \frac{1}{x})^{3} (\frac{x}{4} + 1 + \frac{1}{x ^{2}})

Vereinfache

4 (\frac{x ^{2}}{8} + x - \frac{1}{x})^{3} (\frac{x}{4} + 1 + \frac{1}{x ^{2}}) : x (\frac{x ^{2}}{8} + x - \frac{1}{x})^{3} + 4 (\frac{x ^{2}}{8} + x - \frac{1}{x})^{3} + \frac{( x ^{3} + 8 x ^{2} - 8 ) ^{3}}{128 x ^{5}}

= x (\frac{x ^{2}}{8} + x - \frac{1}{x})^{3} + 4 (\frac{x ^{2}}{8} + x - \frac{1}{x})^{3} + \frac{( x ^{3} + 8 x ^{2} - 8 ) ^{3}}{128 x ^{5}}

d er i v a t i v e \frac{9}{t ^{2}} - \frac{3}{t}

\int sin^{5} (5 x) cos^{3} (5 x) d x

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

in v erse l a pl a ce \frac{( 2 s + 3 )}{s ^{2} + 6 s + 13}

d er i v a t i v e sin (π x)