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

Lösung

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

\frac{5 x ^{\frac{13}{4}} + 24}{4 x ^{3}}

Schritte zur Lösung

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

Wende die Summen-/Differenzregel an:

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

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

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

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

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

Vereinfache

\frac{5 x ^{\frac{1}{4}}}{4} - (- \frac{6}{x ^{3}}) : \frac{5 x ^{\frac{13}{4}} + 24}{4 x ^{3}}

= \frac{5 x ^{\frac{13}{4}} + 24}{4 x ^{3}}

\frac{d}{d x} (e^{4 x^{2}} \cdot 8 x)

d er i v a t i v e f (x) = x^{3} - 15 x

\frac{d}{d x} (3 cos (5 x))

(x + 1)^{^{'}}

\frac{d}{d x} (\frac{6 x}{1 - cot ( x )})