derivative (5x^2+3)^{1/4}

Lösung

ableitung von

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

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

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

\frac{d}{d x} (5 x^{2} + 3) = 10 x

= \frac{1}{4 ( 5 x ^{2} + 3 ) ^{\frac{3}{4}}} \cdot 10 x

Vereinfache

\frac{1}{4 ( 5 x ^{2} + 3 ) ^{\frac{3}{4}}} \cdot 10 x : \frac{5 x}{2 ( 5 x ^{2} + 3 ) ^{\frac{3}{4}}}

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

\int \frac{5 x ^{4} + 5 x ^{3} + 2 x + 1}{x ^{2} + x} d x

x \to 0 lim (\frac{ln ( 1 + 2 x )}{x})

\frac{d}{d x} (sin (3 x) + 4 x)

\int (\frac{1}{x ^{12}}) d x

\int_{0}^{1} sin (x^{2}) d x