derivative 4x^4-1/(4x^4)

Lösung

ableitung von

4 x^{4} - \frac{1}{4 x ^{4}}

16 x^{3} + \frac{1}{x ^{5}}

Schritte zur Lösung

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

Wende die Summen-/Differenzregel an:

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

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

\frac{d}{d x} (4 x^{4}) = 16 x^{3}

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

= 16 x^{3} - (- \frac{1}{x ^{5}})

Vereinfache

= 16 x^{3} + \frac{1}{x ^{5}}

\frac{\partial}{\partial x} (\frac{- 9 x - 7 y}{( 5 x + 3 y )})

\int \frac{1}{9 x ^{2} - 16} d x

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