derivative of 9/x-2/(x^3+1/(x^4))

Lösung

\frac{d}{d x} (\frac{9}{x} - \frac{2}{x ^{3}} + \frac{1}{x ^{4}})

- \frac{9}{x ^{2}} + \frac{6}{x ^{4}} - \frac{4}{x ^{5}}

Schritte zur Lösung

\frac{d}{d x} (\frac{9}{x} - \frac{2}{x ^{3}} + \frac{1}{x ^{4}})

Wende die Summen-/Differenzregel an:

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

= \frac{d}{d x} (\frac{9}{x}) - \frac{d}{d x} (\frac{2}{x ^{3}}) + \frac{d}{d x} (\frac{1}{x ^{4}})

\frac{d}{d x} (\frac{9}{x}) = - \frac{9}{x ^{2}}

\frac{d}{d x} (\frac{2}{x ^{3}}) = - \frac{6}{x ^{4}}

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

= - \frac{9}{x ^{2}} - (- \frac{6}{x ^{4}}) - \frac{4}{x ^{5}}

Vereinfache

= - \frac{9}{x ^{2}} + \frac{6}{x ^{4}} - \frac{4}{x ^{5}}

\frac{\partial}{\partial x} (e^{x y} + \frac{1}{x + y})

t an g e n t 4 x^{2} + 2 x - 1

f (x) = (5 x^{6} + 4 x^{3})^{4}

\frac{\partial}{\partial x} (ln (8 x + 7 y))

y^{^{'''}} - 6 y^{^{''}} + 11 y^{^{'}} - 6 y = x e^{x}