(eginarrayla),,y = left( 9 - 2x ight)left( 2x^3 - 9x^2 + 1 ight)\b),,y = left( 6sqrt x - dfrac1x^2 ight)left( 7x - 3 ight)\c),,y = left( x - 2 ight)sqrt x^2 + 1 \d),y = an ^2x - cotx^2\e),,y = cos dfracx1 + xendarray)


Phương pháp giải - Xem đưa ra tiết

*


Sử dụng các quy tắc tính đạo hàm của tích, thương, luật lệ tính đạo hàm hàm số hợp và bảng đạo hàm cơ bản.


Lời giải đưa ra tiết

(eginarrayla),,y = left( 9 - 2x ight)left( 2x^3 - 9x^2 + 1 ight)\y" = left( 9 - 2x ight)"left( 2x^3 - 9x^2 + 1 ight) \+ left( 9 - 2x ight)left( 2x^3 - 9x^2 + 1 ight)"\= - 2left( 2x^3 - 9x^2 + 1 ight) + left( 9 - 2x ight)left( 6x^2 - 18x ight)\= - 4x^3 + 18x^2 - 2 + 54x^2 - 162x - 12x^3 + 36x^2\= - 16x^3 + 108x^2 - 162x - 2\b),,y = left( 6sqrt x - dfrac1x^2 ight)left( 7x - 3 ight)\y" = left( 6sqrt x - dfrac1x^2 ight)"left( 7x - 3 ight) + left( 6sqrt x - dfrac1x^2 ight)left( 7x - 3 ight)"\ = left( 6.dfrac12sqrt x - dfrac - left( x^2 ight)"left( x^2 ight)^2 ight)left( 7x - 3 ight) + left( 6sqrt x - dfrac1x^2 ight).7\ = left( dfrac3sqrt x + dfrac2xx^4 ight)left( 7x - 3 ight) + 7left( 6sqrt x - dfrac1x^2 ight)\= left( dfrac3sqrt x + dfrac2x^3 ight)left( 7x - 3 ight) + 7left( 6sqrt x - dfrac1x^2 ight)\= 21sqrt x - dfrac9sqrt x + dfrac14x^2 - dfrac6x^3 + 42sqrt x - dfrac7x^2\= dfrac - 6x^3 + dfrac7x^2 + 63sqrt x - dfrac9sqrt x \c),,y = left( x - 2 ight)sqrt x^2 + 1 \y" = left( x - 2 ight)"sqrt x^2 + 1 + left( x - 2 ight)left( sqrt x^2 + 1 ight)"\ = 1.sqrt x^2 + 1 + left( x - 2 ight).dfracleft( x^2 + 1 ight)"2sqrt x^2 + 1 \= sqrt x^2 + 1 + left( x - 2 ight).dfrac2x2sqrt x^2 + 1 \ = sqrt x^2 + 1 + left( x - 2 ight)dfracxsqrt x^2 + 1 \ = dfracx^2 + 1 + x^2 - 2xsqrt x^2 + 1 \= dfrac2x^2 - 2x + 1sqrt x^2 + 1 \d),y = an ^2x - cot x^2\y" = left( an ^2x ight)" - left( cot x^2 ight)"\ = 2 an x.left( an x ight)" - left( x^2 ight)".dfrac - 1sin ^2 x^2\= 2 an x.dfrac1cos ^2x + dfrac2xsin ^2x^2\ = dfrac2sin xcos ^3x + dfrac2xsin ^2x^2\e)y = cos dfracx1 + x\y" = left( dfracxx + 1 ight)".left( - sin dfracxx + 1 ight)\ = - sin left( dfracx1 + x ight).dfracleft( x ight)"left( 1 + x ight) - x.left( 1 + x ight)"left( 1 + x ight)^2\= - sin dfracx1 + x.left( dfrac1 + x - xleft( 1 + x ight)^2 ight)\= - dfrac1left( 1 + x ight)^2.sin dfracx1 + xendarray)