derivative of ((sqrt(5x^4+x^2))/2)

Lösung

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

\frac{10 x ^{2} + 1}{2 5 x ^{2} + 1}

Schritte zur Lösung

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

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

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

Wende die Kettenregel an:

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

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

\frac{d}{d x} (5 x^{4} + x^{2}) = 20 x^{3} + 2 x

= \frac{1}{2} \cdot \frac{1}{2 5 x ^{4} + x ^{2}} (20 x^{3} + 2 x)

Vereinfache

\frac{1}{2} \cdot \frac{1}{2 5 x ^{4} + x ^{2}} (20 x^{3} + 2 x) : \frac{10 x ^{2} + 1}{2 5 x ^{2} + 1}

= \frac{10 x ^{2} + 1}{2 5 x ^{2} + 1}

(1 + x^{2}) (1 + y^{2}) d x - x y d y = 0

\int (6 sin (3 x) - cos (2 x)) d x

\int x - 4 d x

x \to 0 + lim (\frac{3}{x ^{2} - x})

\int \frac{16 s + 16}{( s ^{2} + 1 ) ( s - 1 ) ^{3}} d s