Turunan 3
Contoh 4 :
Turunan pertama dari
![\fn_jvn f(x)=\sqrt[3]{x}](https://lh3.googleusercontent.com/blogger_img_proxy/AEn0k_tsaXfnMJ-Dd3bMhnlrRiiAemAyHKNNdZD-gS0qD16i0rfOEdmdMfuBnUjs1Ji20IfztmUe3jKde45DCwJeSIa1LDvrZJ9Nz7VdlB73Mlt3IgI_5FXMhMQTgEbxu4B15CDsS1MlhyCrvHsIWA=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_tTWtEC9zro_B_iNUswJuGt0YfxHOOu31yF6wbzbNkD8wOaWmwxacYds03tPXh0VhNED3JyvmAvlObn_fTZxJFMXxpdc7Bk5zjA0937AVA5vV8NZTK1fQskA7HMiXQl6MiPB2Ag58kWvK6aEgGs3HWLxH1XSfbmvI5c5DuFz-OVDjrIqLUwHOCWf82vKGMolJRo0T7MSJ4xE9aqHzXqeFSi9F32SjsF0wz_-PRhA3A3Rq9j0pMm-7cbRY3saQ0qHu5OXBmBKznu8zAGn4gqKGrOrGjfrlhT=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_u4zAjDjItXaRzhJgmIqerCwCDSrcN4LInX6tpoLdE3hibLqclKE1D2elcXLqY7vzSdF1tRsdicJhkX0WrA5k-QmEuEOjnod6UKJ2i-TCY5-C9bQExk6yZ1iG3AlZ7z77_4u20h27IVCD8FfE5Ozf-TJ0KpD4EAYmtAUtehIpLosKE2SJe6N5GLyaqt4X3Qx7cxiuU8ER7iuQXh-weZ-7Mg8Drgjb-K6L2-giABBFUVYmywUw1HFvc0DiEEZN2DD4qMpqaRyexTIMiIUKUwXZsdYmVmJ9xUAfHL-56ORhjYnDpaQkpBphxDh5PWRP6uNxg-IzK14mf4vIwHLTfL-4X16iiVS-885easNLvSsy7RaSVjglNLQjVBdQWOS7SUG9Pn4CH7HGzz4AO3C1nsVNTbZFMT3K4FnC92cQALjjJtB4hBqcxiE_olBwAca5pj-LczBAMlevKs6JvLdYI1LraOA-sJQeixqQ0T0Nq0fI1qyWEdbTehd01-rFDluaDHULdStRollHAFBISMqvj1_2gbJAZzS82fxWV99it9d0XtJ_NyQsdzA0uEVkmbAjyRCLM1TLqOx3kQLFrfooqjTaVW0VJW4gLApCB3XfPLZoLZ=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_uQMewGKNxG1oRkLR2A9ojXsfXlFPkZxo0xzgAUM1huG1yUQvaL3Gs1_k1Gj93-KriZk4Gtq5BtPbegC2iAb57spjcR79tcqSVkUM94DCgxU5oRNFOmTn6PBYBpQ7I4OLXhOxoKJG-C8OBTIuiIHEtDgwAJR8fidByAUSvsBTS3gUph18Usgjhz0vCH1PbKCPAE5qKumxzsXQae8a6KovslIJSwbqOQXR4Aus61KS6_Et7NxBpafgOD2eRH0L-J5lthnEkV4tQ8q9Insaaqbbp3tyDbdLTKKEiChUWvehZMIRe1vSYs2yeVKCLE171UsIZJ8M0KMy7rpBHOgz038AX66oShvueTBh4KKP1jSxPhcU4C5LFfvqUv02Rj-Sj0oAki1nYDG5xf-w=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_uK2yihLBLIDC4EN-pJQCYvomZUq2DZXRJQiNnUK3Mo6Ua0IOzlF6YslOzTm_4RuOrgHeLtURGzmpEEPOly_53bTZ2xY9GDatWyEWB6lMPRXhEPM7Tl4HB79lBxthIccqZ1BYtxjKsUSr_GpmG588VALDB5F4nI9RKunz1CuCjSBVph9BMt5h3XOmgN7q7-BclyE6O89AXeonZzAOHQv7p_dH83RGMgGSr6LHrVgSybt_nUP0Cd7alGZujcWkq57ungHZmThLy9DT3ffSSJdfTFn-FTtUvJhL7QN5cSLw9y6gT1ScjvLui5Ypn5EdY5ZwYlQrpi6koGFmlr8_Bb2ZxqW65zlE8SLVHKwYDmpKX7C6lVEbPRFdSALKV0m62VfQ7YLtTndQ=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_tRp-cYzmzwaXiStxpi4l7R7Y3aeaNWEWiUIog9KW5Z0joHeKK1NtR4bA8iuSC0YGV3L2n7ALngMGLESuToC-Y1Xc_FayfLfzzst3EEpt6_j_aHbqt-5ERDTfFyYPRT8LBUA_huNcpXrlPugo1veD1UTOs37J2gLBng61q0if5grSYevZS1jw9SR0ns5NfDvd1gACl8qF8zy90Fqsv2eXoc8J0Yl-l5JDlm4Fp7mCGxv1rlhFHMXeE_D1b0QizntqrwU8N64z1TiMGaTaqI5OO5dHHe3SwN2vrWFhBWgC727kRpUvJWPP7ZRVOV_SKYW45182MoNiw45bgklH0df_38F5Ls_nmWEf91kJe3jq8=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_sDRUg7MN_CF4sDy9zck_UpYMmSojfK0tzwNqZ0x4tLRxyrPERXJ9geKaCz52TGZ41yetKi1O1VM1o9PqmNr4Dx_bz6FsPeM1ZYfu5HGHrexp_tMHg7H-lFt1JjT49LJtMWx9eMyhwgypt3nspAkaD7QV2_RjzVAEcQSLw_AFjcs4EG9_VyKzP7g1g9xiffnRwVQ0zm9Yi1UOB2kHcsjFmPpDvdJcNhKFI41C8TDNV-zAGZ95ThZiKSC_4nTF8r1zRuv_gp3wzgMeo4=s0-d)
![\fn_jvn f'(x)=\frac{1}{3\sqrt[3]{x^{2}}}](https://lh3.googleusercontent.com/blogger_img_proxy/AEn0k_vzLKN5NYp_9wTS_kyHrg6z0s86gfzdEI4JRAMLCSPB7MyTJ_hOM3uFcCNvqxCRW_LQjBwPegOf0i7VPiFu6l8tqiLzTxCOBAxK-6DFrdyceEAu2kPkqArvpJqaFxhRpM0e7Fw_2LRNtfz5zOBBORu5Kv5SqSMh_bo99hH3tbWzMYpJY7Hk84li1pFp=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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