Turunan 3
Contoh 4 :
Turunan pertama dari
![\fn_jvn f(x)=\sqrt[3]{x}](https://lh3.googleusercontent.com/blogger_img_proxy/AEn0k_s-EY7Jphz_QFJ4kR9YCVV56xeLyYGqP3rzwrjcXO-il4kJFzK2jcENFM1ntzpAj1eJELS5koVWo4NBiABa4mEFBvy0eq86X9zPb_XLMn1i4SMz8EBIozNwUd2HHsCDIn1hTroRZPue7BNr9A=s0-d)
adalah
Jawab :

![\fn_jvn f'(x)=\begin{matrix} lim\\h \to \0 \end{matrix}\frac{\sqrt[3]{x+h}-\sqrt[3]{x}}{h}](https://lh3.googleusercontent.com/blogger_img_proxy/AEn0k_sEgnsTmaGJ1yM49njqgIYx0Dq9FKP_HC2_qUf867l1GcTf66r4Ibac-EtuvxmzFD183zkgbiKYQJcFVIC_nIKPZ3X66N9C41eL4oByjggCUYxoKRbCLvSGAlYncGdeak6K8se7HObUptZnqEdIob8SAw0U_4_FNXiCxVqM_KHNgYkmmo1GO9Z18DiY0-Fre6z81IplvHryY5ODpAbrktAGtpE004yOisSBITH02yUi934NjtOHivWvGD8tcfMyczrnprJkop0SkIhuQnwaDfqO9axZLDjA=s0-d)
![\fn_jvn f'(x)=\begin{matrix} lim\\h \to \0 \end{matrix}\left ( \frac{\sqrt[3]{x+h}-\sqrt[3]{x}}{h} \right )\left ( \frac{\sqrt[3]{(x+h)^{2}}+\sqrt[3]{(x+h)x}+\sqrt[3]{x^{2}}}{\sqrt[3]{(x+h)^{2}}+\sqrt[3]{(x+h)x}+\sqrt[3]{x^{2}}} \right )](https://lh3.googleusercontent.com/blogger_img_proxy/AEn0k_tDLMw7GPv18fDvrzsjR3mMIYCJZmn9CSJl_d_SSZZ4t9TdyKf7A97r4G8iZ2dZcm-Gqcc4Cz8nQS7yXpvtOpjE2T_ynSbxN66KHLePF2PZackrdFw0AefEkyFMICDSqFqoMAn-l29x171k7Du0OuoVWVsQdMhBmrZShQSinHBz-LceyrOs5nKtc9_JYmWfj0Snf-fMLFZpUcDuUVzGtkKDewTACHjBHsvGZwS3VC4E7I4lIz9fqr8TIZiywyJvtR1RbVM1kjzBla6UmEzFALBjO7X2iZDznM-opPN18UgIq7gf-3Bfa5kbE0M_gB2p8NdWUJfUGClv_hLX60mKRJGcM2H7fnvucZxI0_lb5xCcv2F5zkyNuiXGQuv4mULuue2gzhmYycMWoki4lLQ2b3DYA16surxTShQpIPLqZzeM8zvscT5iqOWAnsDPXZEhNnowHjVilY03ght_MhP7cSgTpVCV548xZcllbBsny7toV5TkgBx4-E_nqY7fFrL_7eB2SjY0OoNEGBwhJ9y7BZv6DoK-MhTlzxGjdgekR_bf6JYWiasRn61s15mQBcDer2XH8nlu86No05KrUh7XTFrZLxbv64j_UrXd85xj5cna=s0-d)
![\fn_jvn f'(x)=\begin{matrix} lim\\h \to \0 \end{matrix}\left \frac{x+h-x}{h\left ( \sqrt[3]{(x+h)^{2}}+\sqrt[3]{(x+h)x}+\sqrt[3]{x^{2}} \right )}](https://lh3.googleusercontent.com/blogger_img_proxy/AEn0k_stMAx7mBWkP7Zh0dhPzdFyXVuj8FXt_bBSG6Jsmo3k9DZmiRkKYUkO3oQAduxNFv7Jxo_hUc8v1orohaowkXzeeOOQsyO3EWYY7QKYyNAqUOSJgJg4prRWJKrV8_U-ukxhalKcOIKmONbCg5jvf5sDJ3JXpbBNrBDnTR07Zc8X0SHwUBHaWNpDTD0Vg3ugu3OVLU-EOgE4UaFPvhj-8rPmj3dXK3YkxXFb5lBIuKh1FctVh-DEsZEjdhf0LdkYxMfgDNzmaj_Me6944Vi4NCnRNv-2siWgUADtm-AqNZXbqlBIQpMqcOKneXj5dRrNMeaKDivmy0UkxeG1UO5PMzAj24kdce7ymopJF4yptxLkFFugGNynUw86yGVl8I5_R_-1nhPbQh5SMA=s0-d)
![\fn_jvn f'(x)=\begin{matrix} lim\\h \to \0 \end{matrix}\left \frac{h}{h\left ( \sqrt[3]{(x+h)^{2}}+\sqrt[3]{(x+h)x}+\sqrt[3]{x^{2}} \right )}](https://lh3.googleusercontent.com/blogger_img_proxy/AEn0k_upBXdtJ7MdP9gO4P4KFTxtjagJKIoMr8EfIgNnFjXn7_eMBUUaVSUoHCkxnPJ8i_8Nrca_V2iSgVt9O3rWnXOhtUwgG2jquFiklEK4UGzffYHVhRekw2MyevzPHhuJvDWvr7gzBeLt_pbYBT2diE5IN5Cv5IZT3ZU-rv7zM3F6MD1AschBAU8kFuJUo1y79gIZy-3_FVVPGU4fmzbkmn-XI9Qsc13lQTBM5KPdcg0Yd4tovn_g2YMTnffBfthssV6lnvPoGG1JfJ4YGBJ1WNgGDRjP1srQtFGrlbu0Qc_Dt_78CJNEch4HEMe0puL9FWjSZV7oSCpFraCygUg-3YSTJ7ViV8xRHkHKLnodFUI8jraZSDGxLaTuK9u2OZSYsVq8qLkmSw=s0-d)
![\fn_jvn f'(x)=\begin{matrix} lim\\h \to \0 \end{matrix}\left \frac{1}{\sqrt[3]{(x+h)^{2}}+\sqrt[3]{(x+h)x}+\sqrt[3]{x^{2}}}](https://lh3.googleusercontent.com/blogger_img_proxy/AEn0k_u9qWBnoXQ8AJeFR50jnscYWQYxUi4cCd9eLPQCMFWC8rWyzmF8wZmNELNP1vm7zrLnrQ30u5EVclmio-ue0ssFbppH8QXs0ZuZZSvP25luxAWFBDkwWLvTLgNUJamnUjrm97ps3czmR-35PR-khUkprZ_lpD8jPdpyzkIZmlLlJqieGoZROlpxxsxOCeqx_jSp4pL5dmeuIzNA2RSJEUc4XryziKKgU1MIs7e6kTw82vX4mqp_CpFsJm9561OQsHclp19lBJvRBwj3Ij4zVS5KTbTvRht9YICaMxzUNuYUQ-wGVQ7VMsvTybBQR7EP74DBKqTZF0-4Dp3aHkn7GGw3sxgLz2rpf6uoU5TjOFs=s0-d)
![\fn_jvn f'(x)=\frac{1}{\sqrt[3]{(x+0)^{2}}+\sqrt[3]{(x+0)x}+\sqrt[3]{x^{2}}}](https://lh3.googleusercontent.com/blogger_img_proxy/AEn0k_uoHVI2UqibGI15HwCwXBu69dEHS_ynP8V0TZDDYHnzq6YwNS0EZws-uoMOnJGypa8WOGS15-G555SVJkTLCIjpJFfEDJwZ6X5-dJP7cVZ12A65bRef6ZCSNDlBg49Qkqj7N7twxV8yAVhIgS7NBS38mxOLkxwz79ZADnohAySFusV7cs0Ln2E2mqgS9c6u2GHgJ3iaVQEqT-ed_l5ET2u3Um78-r2_GnNHiLzEza1QqQi-htau4mAzwD81DGipQMCGOdTv-gBaaEJt=s0-d)
![\fn_jvn f'(x)=\frac{1}{3\sqrt[3]{x^{2}}}](https://lh3.googleusercontent.com/blogger_img_proxy/AEn0k_vZlDsZOJ_caw-Kn-V0xg7soDcuB9hcecc_DasAWbO8ng05SmG8ZtEdvTdZy-zBTJmKYLLVUdVkdRrWpT473P7sE_J4uELew-zEdx8rXSdm9XCb3b3-i4GjVtOjPrz5lleBu6mjiwcnVfaAwM54afnR6FuK1VHeeOBS_1aGBpAMPnOvzB6dgxOZkWqS=s0-d)
contoh 5
Tetukan turunan pertama dari f(x) = sin x
Jawab :











Cara II :

Dengan memakai rumus
maka diperoleh



Turunan pertama dari
adalah
Jawab :
contoh 5
Tetukan turunan pertama dari f(x) = sin x
Jawab :
Cara II :
Dengan memakai rumus
sin A – sin B = 2 cos ½ (A + B) sin ½ (A – B)
Komentar
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