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

Lösung

ableitung von

\frac{5 x ^{4} + x ^{2}}{2}

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

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

t an g e n t x + 49

3 x y^{^{'}} - 2 y = \frac{x ^{3}}{y ^{2}}

a re a x, 2 x, - x + 2

l a pl a ce t r an s f or m t e^{- 4 t} cos (5 t)

a re a - x^{4}, x^{2} - 2 x