Question

f:R->R , f(x)= √x^2 + 5 Calculati f ' (2)

Answer 1

Explicație pas cu pas:

$f(x) = \sqrt{ {x}^{2} + 5}$

→

$f'(x) = \left( \sqrt{ {x}^{2} + 5} \right)' = \frac{\left( {x}^{2} + 5 \right)'}{2\sqrt{ {x}^{2} + 5}} = \frac{2x}{2\sqrt{ {x}^{2} + 5}} \\ = \frac{x}{\sqrt{ {x}^{2} + 5}}$

→

$f'(2) = \frac{2}{ \sqrt{ {2}^{2} + 5}} = \frac{2}{ \sqrt{4 + 5} } = \frac{2}{ \sqrt{9} } = \frac{2}{3}$