derivative f(y)=ln(5x^2-x+1)

Lösung

ableitung von

f (y) = ln (5 x^{2} - x + 1)

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

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

\int \frac{v}{3 - 0.001 v ^{2}} d v

\frac{\partial}{\partial x} (y + arctan (\frac{y}{x}))

\frac{\partial}{\partial y} (x^{3} - y^{2})

t a y l or ln (6 x + 1)

x \to \infty lim (\frac{e ^{5 x - 3}}{ln ( x - 2 )})