derivative of (12/x-4/(x^3)+1/(x^4))

Lösung

\frac{d}{d x} (\frac{12}{x} - \frac{4}{x ^{3}} + \frac{1}{x ^{4}})

- \frac{12}{x ^{2}} + \frac{12}{x ^{4}} - \frac{4}{x ^{5}}

Schritte zur Lösung

\frac{d}{d x} (\frac{12}{x} - \frac{4}{x ^{3}} + \frac{1}{x ^{4}})

Wende die Summen-/Differenzregel an:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (\frac{12}{x}) - \frac{d}{d x} (\frac{4}{x ^{3}}) + \frac{d}{d x} (\frac{1}{x ^{4}})

\frac{d}{d x} (\frac{12}{x}) = - \frac{12}{x ^{2}}

\frac{d}{d x} (\frac{4}{x ^{3}}) = - \frac{12}{x ^{4}}

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

= - \frac{12}{x ^{2}} - (- \frac{12}{x ^{4}}) - \frac{4}{x ^{5}}

Vereinfache

= - \frac{12}{x ^{2}} + \frac{12}{x ^{4}} - \frac{4}{x ^{5}}

y^{^{''}} + 2 y^{^{'}} + y = 0, y (2) = 1, y^{^{'}} (2) = - 2

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