Question

Найти f'(x)
f(x) = (5x-4)⁶*√(3x-2)​​

Answer 1

$f(x)=(5x-4)^{6} *\sqrt{3x-2}$

$f'(x) =((5x-4)^{6})' *\sqrt{3x-2}+(5x-4)^{6} *(\sqrt{3x-2})' =\\ 6(5x-4)^{5} *5*\sqrt{3x-2}+(5x-4)^{6} *\frac{1}{2\sqrt{3x-2} } *3=\\30(5x-4)^{5} *\sqrt{3x-2}+ \frac{3(5x-4)^{6}}{2\sqrt{3x-2} } =\\\frac{60(5x-4)^{5} *(3x-2)+3(5x-4)^{6}}{2\sqrt{3x-2} }=\\\frac{(180x-120) (5x-4)^{5}+3(5x-4)^{6}}{2\sqrt{3x-2} }$