derivative f(x)=\sqrt[4]{x^5-x^3-2}

Lösung

ableitung von

f (x) = 4 x^{5} - x^{3} - 2

\frac{5 x ^{4} - 3 x ^{2}}{4 ( x ^{5} - x ^{3} - 2 ) ^{\frac{3}{4}}}

Schritte zur Lösung

\frac{d}{d x} (4 x^{5} - x^{3} - 2)

Wende die Kettenregel an:

\frac{1}{4 ( x ^{5} - x ^{3} - 2 ) ^{\frac{3}{4}}} \frac{d}{d x} (x^{5} - x^{3} - 2)

= \frac{1}{4 ( x ^{5} - x ^{3} - 2 ) ^{\frac{3}{4}}} \frac{d}{d x} (x^{5} - x^{3} - 2)

\frac{d}{d x} (x^{5} - x^{3} - 2) = 5 x^{4} - 3 x^{2}

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

Vereinfache

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

= \frac{5 x ^{4} - 3 x ^{2}}{4 ( x ^{5} - x ^{3} - 2 ) ^{\frac{3}{4}}}

x \to + 0 - lim (\frac{e ^{x}}{x ^{3}})

n \to \infty lim (5^{n})

\frac{\partial}{\partial y} (x^{2} - x y + y^{2})

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\int sec (2 x) \cdot tan (2 x) d x