Câu 7: Tính đạo hàm
của các hàm ẩn
định bởi:
a) y= x + acrtg y
Lấy đạo hàm 2 vế ,ta có:
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh40LLvwRYNLbp0rOG7H-vux2-e6MwrLZvJTRjfug-V8OIgRtD9ti-XQKElXacDPgne34ORN2fzRiSIGcCMDf5Ad4khsPu15jRrZHssfjzL93WSPksFx8KsswBzu94noHbnFrj658EwfmY/s320/image003-771639.png)
Suy ra:
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEitBnjANEs_NSHzBGZSn55o7q-zqmrAqpgENkTmZXzD4hXd8vQP4Gx31tEJoP5XiZlEusT1YDR3jQuFdyQKbBaEvXuPgEMsBKCLjsVOTfQvcVFONnmE9ZsmKafRMIaMi_uFiSDu0y7VGWY/s320/image004-783317.png)
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj4qursluH9bYQdkhucw8Mn5cSOKPEgu4Y3ipJimSyhWE09lguKQr9w6wYXfuHMgNDwDWDS6DrgYmkLirSq3azdJaO9MhD7UwTZhGsUPxgqHrx1Jyu6US3yaubmMb3ddPCVHZPJj1spZ9g/s320/image005-785382.png)
Vậy:
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhnTUUKtnpNgqBCt9ZM1X8nhpWC2Yj9l27DvDB6bglREVQHny4E-Pd6tooNggqyDXIXmj8wHUnYjBQhbBBlc2QhgrDQh-hAPygVxhwpHDISGURA6k6LMHHPiMjsBD4f3gNBaXlbHUdIv5U/s320/image006-788403.png)
b) y = 1+ y![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiWUAXMM_AI4sj2tvSZ6Lacn7hCpvQvcoC3U35CiF4AKjxSWbeK1R8u-TTCnjtrBnNKrCu7xTQTltschd7zBiM4nfKVuIazutKVpOJHmIjfHRHwZHdv6voWxSId_VYyjPw-5zSrCas5VNE/s320/image007-791472.png)
Lấy đạo hàm 2 vế ,ta có:
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEipPIlx9X_8TEiqYPXeOsbxqU_hJ8cOQ2t722zT_um4XnXGnDTX0fZImYetiw4y27V2OW2sECtz-doAHkJupHJHRTjf6zHXcQOetj1E9T9mZltVSEjeeOICd8oubcPOezQpzue9WtFmWqw/s320/image008-793238.png)
Suy ra:
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiZOEu8ICWVwID9QCZtzXUzRgrTSPMakFiKVilXzEQkCqFRFT6rFNZn5jTFMcVaFwRTpN4X1UHiyjVgabMfEmRtVaTef35QuXnLh9r_pnG0teU8Yxc6Dmcp3JhDv3xOZkMTZEDiUxwvamI/s320/image009-796964.png)
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgNDl6wIISNbfynmlrmXsd7UX7VEpotq7DQ21Q-h07IYJNP1_B61reoCXmpWGJ33O3rOx4seeQsEISC0GcLMLC4NGaUgaVTqpgQ8uN6eSLj4eL6zri5KRwo-_s4TEAQ1AmlBcO-Gm42LT8/s320/image010-799006.png)
Vậy:
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgpsJIm3iWgaw6yymEK5Mtp9bEnRxtJxqRN3k4kt-mN89M0b20X6YYSpXiAkZXH3fwnDxAwubkgj9TlCqcNQIvt3EeT8jWDufKi2tbianjEOHrjhfddgd0cdNyRJPioiJs0hC9KBrkXM5g/s320/image011-701437.png)
c)
. Xác định y'(0)
Ta có:
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg6booJ5PSfg8giDlOdlaZ3lqmrLR6ulFgexUUTsjZD7kts_-EU5-E1Jmw4bqYSFclG76haRWXf38ok50DY8DlrhZ0DXQzgz8FVIN5_WvjEl-iwsSYMaYMA0-_HLBUpByXFbhaF8ZpUuIY/s320/image013-710128.png)
Suy ra:
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgHBhafZM8EkIM9w4gTLj49Q3D1gvgUH70AtAsKVrN1JcZI3kgi_vrfpSRbXf-cn5r9_1rrURdZm0RJhv5gAikfwukNFRDEnuh2tHKWvCMavWISTvMmEmqopUpbUNGC65_9I6GB97JUe_I/s320/image014-714412.png)
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgiVAuqVqGUvx-fU9e12pHF-sZXhIRYl4ZlcxMiJ1VY-BS9aCh8ZmdGjIsCMmsMohwfOKbc8TEPHCDQmpQyE_IaO8FeGKPL3Y0N7mgWOS7MJkQhon7uzjKPHUOSe8U2Is80AlqbTpjIHcM/s320/image015-718108.png)
Vậy:
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEieIItPoSXpJ6xVHkwNJ1jXm5Kv6tu07f7ueEWZ-VpTu3IJjTGycpPUjZEAMUCxdr-Pqzm_q3rDw_iiZ8qUrVqSBTDCWFG6Rr6znyMAzapWrs6QP_ADDH6ULijEtjGPXl9idNT78U7Kaoo/s320/image016-720646.png)
Khi ![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjykpQEHEc0jaZ5N6-ubwVpqqxz-iS1CVkYuJ6nCNjBtbzxD24FjK8y_XGKdgSCMSmpXZVuQ4F-gKwHH3lCB-hgzCO8eAhBLlb-yx_uNAfLnXGeMDLF9we0aBopSeqWieO0IPoJDXmGTbg/s320/image017-725004.png)
Thay vào, ta có:
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjla2TRnGBsgGDxmpg285d-ZpZXq_kbV9Sij9W-OVwIfGxrpRsWfwwpeQfSypgYOpdnp1qUMFZHwHkJ3rN7vMbQ7jeqdUqGRxgtDAF05gYDf8PSze3JWD4hNLDzE3YWJfHkjURGZpbPyqQ/s320/image018-730757.png)
d)
. Từ đó xác định ![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh2G5RJxn-2HOqahzYeMxRkuzFiJB_g9NIkUxFe_NBXx1kVKILNdbquUFZJJPF4OKJRDc4laVIjG9xKvVwSNq5uUSKJ_xumuhlrs08DusSUz5hXUnSzYTSutetswzWfhGJe6JqT2DmcsRM/s320/image020-734651.png)
Ta lấy đạo hàm 2 vế:
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiuklQ2NOGEdIxNKkBrrsmJgx3s-69BRUgoJ-ObNbUnwPtnV_PlHZZmjLRotQOFGyGCW7Bb9dHY5vUJ9HL_jZrIgWHLCD5ZxgblQp49Z52qQSk2WWZ1RXY_gWlyl2iR1A30IvHXjWkSxEs/s320/image021-737886.png)
Có được:
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgWQkww-XXFkPidDbBfTSRqr30g59XIHayGpOgt2jybRatyrH2oZ-zkXmtHm2UqTvYbJiy_7EFH7mSDqtuKv597dlx0lP2Xrjf3z5QPtarbXynH2Q3qm3_KIM7zAK4DdG4gwC09LRgHemE/s320/image022-740803.png)
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgFaRj2V1Di0hTGUZCSto6q3pgOUkcgNN2Q-YBOCFF0jiJy7S4JxscmPaOHDpQmtlQla_qCo9XQcbtiSNwwVpZRlRcX5OzIVN5pCUqXCdwqCysTv3rDbJYpKq-tLOp1_RWUEN75tAPdVAM/s320/image023-744468.png)
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhoJfWCX3z6dc8PYYd4ZyZ0gMTbPyNIs9PFmA-v1NqlcKNDiZWTtqyu676mAw3errkBiUuY1OdygjJMRmw1JxbwJ01_iZB8ArNpkayAFtsP4iLFhQbQ16I2vUL5n6H5cuTwRvehM6hfURo/s320/image024-751426.png)
Xác định ![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgf5MC7-cd4Ut6BREGe5NsB8eNmBcsT_L-M0iNOJyU8Aalv2B3zmEyFg3FeNrLrqdLIw9SxI7Eor1gwHDJ3908LCXAWtuNf7C43GwIHJ7orpLE2J6cQ3lqNcXEjYHKDr8E7MTiPxZgN2Zo/s320/image025-755135.png)
Khi
, tính được
. Thay vào, ta có:
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg6UpQFlW-qTYS8lcCih2CjqqoT4FfGXZtSM3_gibaK_hLCN2SoPujVR7B3nhAKWSpjNQBJuJikEM6vR56oNt8K_ttpc9r05_2mp0eqSL9zkSBi7Hpky9y5CP_1E-5xQemKIHxNfe-W4qU/s320/image028-765291.png)
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