(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 bỏ ra tiết
Sử dụng các quy tắc tính đạo hàm của tích, thương, nguyên tắc tính đạo hàm hàm số hợp với bảng đạo hàm cơ bản.
Lời giải bỏ 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)