Question

f(x)＝x²log3x
f(x)＝ln²x
Ajutor la rezolvarea derivatelor

Answer 1

$f(x) = {x}^{2} log_{3}(x)$

$f'(x) = ( {x}^{2} log_{3}(x) )'$

$f'(x) = ( {x}^{2} )' \times log_{3}(x) + {x}^{2} ( log_{3}(x) )'$

$f'(x) = 2x \times log_{3}(x) + {x}^{2} \times \frac{1}{xln3}$

$f'(x) = 2x log_{3}(x) + \frac{ {x}^{2} }{xln3}$

$f(x) = {ln}^{2} x$

$f(x) = lnx \times lnx$

$f'(x) =(lnx)' \times lnx + lnx \times (lnx)'$

$f'(x) = \frac{1}{x} \times lnx + lnx \times \frac{1}{x}$

$f'(x) = \frac{lnx}{x} + \frac{lnx}{x}$

$f'(x) = \frac{2lnx}{x}$

$f'(x) = \frac{ln {x}^{2} }{x}$