derivative f(x)=sqrt(5x^2+3x+8)

Lösung

ableitung von

f (x) = 5 x^{2} + 3 x + 8

\frac{10 x + 3}{2 5 x ^{2} + 3 x + 8}

Schritte zur Lösung

\frac{d}{d x} (5 x^{2} + 3 x + 8)

Wende die Kettenregel an:

\frac{1}{2 5 x ^{2} + 3 x + 8} \frac{d}{d x} (5 x^{2} + 3 x + 8)

= \frac{1}{2 5 x ^{2} + 3 x + 8} \frac{d}{d x} (5 x^{2} + 3 x + 8)

\frac{d}{d x} (5 x^{2} + 3 x + 8) = 10 x + 3

= \frac{1}{2 5 x ^{2} + 3 x + 8} (10 x + 3)

Vereinfache

\frac{1}{2 5 x ^{2} + 3 x + 8} (10 x + 3) : \frac{10 x + 3}{2 5 x ^{2} + 3 x + 8}

= \frac{10 x + 3}{2 5 x ^{2} + 3 x + 8}

\frac{d}{d x} (e^{- \frac{x}{5}})

\frac{d y}{d x} + y = \frac{1 - e ^{- 2 x}}{e ^{x} - e ^{- x}}

\int x (4 x - 3)^{10} d x

f (x) = ln (2 x + 1)

x \to \infty lim (3 x^{2} + 2)