[tex]f(x) = {x}^{2} log_{3}(x) [/tex]
[tex]f'(x) = ( {x}^{2} log_{3}(x) )'[/tex]
[tex]f'(x) = ( {x}^{2} )' \times log_{3}(x) + {x}^{2} ( log_{3}(x) )'[/tex]
[tex]f'(x) = 2x \times log_{3}(x) + {x}^{2} \times \frac{1}{xln3} [/tex]
[tex]f'(x) = 2x log_{3}(x) + \frac{ {x}^{2} }{xln3} [/tex]
[tex]f(x) = {ln}^{2} x[/tex]
[tex]f(x) = lnx \times lnx[/tex]
[tex]f'(x) =(lnx)' \times lnx + lnx \times (lnx)'[/tex]
[tex]f'(x) = \frac{1}{x} \times lnx + lnx \times \frac{1}{x} [/tex]
[tex]f'(x) = \frac{lnx}{x} + \frac{lnx}{x} [/tex]
[tex]f'(x) = \frac{2lnx}{x} [/tex]
[tex]f'(x) = \frac{ln {x}^{2} }{x} [/tex]
