Bài 4 trang 169 sgk toán 11

(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 những quy tắc tính đạo hàm của tích, thương, quy tắc tính đạo hàm hàm số hợp cùng bảng đạo hàm cơ bản.

Lời giải chi 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)