derivative y= 4/x+sqrt(x+0.5)-5x

Lösung

ableitung von

y = \frac{4}{x} + x + 0.5 - 5 x

- \frac{4}{x ^{2}} + \frac{0.5}{x + 0.5} - 5

Schritte zur Lösung

\frac{d}{d x} (\frac{4}{x} + x + 0.5 - 5 x)

Wende die Summen-/Differenzregel an:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (\frac{4}{x}) + \frac{d}{d x} (x + 0.5) - \frac{d}{d x} (5 x)

\frac{d}{d x} (\frac{4}{x}) = - \frac{4}{x ^{2}}

\frac{d}{d x} (x + 0.5) = \frac{0.5}{x + 0.5}

\frac{d}{d x} (5 x) = 5

= - \frac{4}{x ^{2}} + \frac{0.5}{x + 0.5} - 5

t \to 0 lim (\frac{sin ^{2} ( 3 t )}{t})

\frac{\partial}{\partial y} (\frac{1}{x ^{2} + y ^{2} + z ^{2}})

n = 1 \sum \infty \frac{5}{1 0 ^{n}}

d er i v a t i v e y = 14 x

\int_{1}^{5} \frac{x ^{2} + 2}{6 x - x ^{2}} d x