Question

Derivadas??

$a) f(x)= \frac{13x^{2} }{2}- x^{3}-12x b) f(x)= x^{4}+4 x^{3}-2 x^{2} -12x$

Answer 1

$a)\ f_{(x)}=\dfrac{13x^2}{2}-x^3-12x\\\\\\ Derivada\ pela\ regra\ do\ tombo-\ desce\ o\ expoente\ e\ reduz\ em\\ \ ~~~~~~~~~~~~~~~~um\ no\ expoente:\\\\ f'_{(x)}=(2)\dfrac{13x^{2-1}}{2}-(3)x^{3-1}-12x^{1-1}\\\\ f'_{(x)}=(\not2)\dfrac{13x^{1}}{\not2}-3x^{2}-12x^{0}\\\\ \boxed{f'_{(x)}=13x-3x^{2}-12}$




$b)\ f_{(x)}=x^4+4x^3-2x^2-12x\\\\\\ Derivada\ pela\ regra\ do\ tombo-\ desce\ o\ expoente\ e\ reduz\ em\\ \ ~~~~~~~~~~~~~~~~um\ no\ expoente:\\\\ f'_{(x)}=(4)x^{4-1}+(3)4x^{3-1}-(2)2x^{2-1}-(1)12x^{1-1}\\\\ f'_{(x)}=4x^{3}+12x^{2}-4x^{1}-12x^{0}\\\\ \boxed{f'_{(x)}=4x^{3}+12x^{2}-4x-12}$


Bons estudos!