derivative of 1/(4x^3-6/(5x^4))

Lösung

\frac{d}{d x} (\frac{1}{4 x ^{3}} - \frac{6}{5 x ^{4}})

- \frac{3}{4 x ^{4}} + \frac{24}{5 x ^{5}}

Schritte zur Lösung

\frac{d}{d x} (\frac{1}{4 x ^{3}} - \frac{6}{5 x ^{4}})

Wende die Summen-/Differenzregel an:

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

= \frac{d}{d x} (\frac{1}{4 x ^{3}}) - \frac{d}{d x} (\frac{6}{5 x ^{4}})

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

\frac{d}{d x} (\frac{6}{5 x ^{4}}) = - \frac{24}{5 x ^{5}}

= - \frac{3}{4 x ^{4}} - (- \frac{24}{5 x ^{5}})

Vereinfache

= - \frac{3}{4 x ^{4}} + \frac{24}{5 x ^{5}}

\frac{d y}{d x} = (\frac{2 y + 5}{8 x + 7})^{2}

y^{^{'}} - 3 y = 3 e^{4 t}

2 x + y + (x + 2 y) \cdot y^{^{'}} = 0

t an g e n t f (x) = 4 x^{2} + 5 x - 5

n = 1 \sum \infty \frac{( - 1 ) ^{n + 1}}{n ^{5}}