Question

derivada de ln(x^3+5x^2+8)

Answer 1

$f(x) = \ ln(x^3 \ + \ 5x^2 \ + \ 8)$


Derivando pela regra da cadeia:

$f'(x) = \ \frac{1}{x^3 \ + \ 5x^2 \ + \ 8} \ . \ (3 \ . \ x^{3-1} \ + \ 2 \ . \ 5x^{2-1} \ + \ 0)$

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

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

$\boxed{\bold{f'(x) = \ \frac{3x^{2} \ + \ 10x}{x^3 \ + \ 5x^2 \ + \ 8}}}$