Question

Se considera funcția f:R ->R
f(x)=ln (x^4 +1)
•Calc f'(x)

Answer 1

Ai formula, ln u=1\u * u' , unde u este o functie , in cazul tau u= x^4+1
f'(x)=1\ (x^4+1) *(x^4+1)'= 1\ (x^4+1) * 4x^3=4x^3\(x^4+1)

Answer 2

$\displaystyle \mathtt{f(x)=ln\left(x^4+1\right)}\\ \\ \mathtt{f'(x)=\left[ln\left(x^4+1\right)\right]'= \frac{\left(x^4+1\right)'}{x^4+1} = \frac{\left(x^4\right)'+1'}{x^4+1}= \frac{4x^3+0}{x^4+1} = \frac{4x^3}{x^4+1} }$