Turunan 3
Contoh 4 :
Turunan pertama dari
![\fn_jvn f(x)=\sqrt[3]{x}](https://lh3.googleusercontent.com/blogger_img_proxy/AEn0k_shyGD8ZFwdH_w3PoKbB722NLUx-xMESf-_IzhF4ydOqwiKuxkrsmhgIQl_iwFO34SiFSYhn0fsAyFDlosUgA0VCdCOZ-McXW1PMqwxJBCoIm_0Pyd9wEOcHFIqghhjvnqdDi4FH0zsKYZjYg=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_tKpL8y6it_FVgxlEUuhtnDnax9nk6NIgaCsLNSQ5y_gd-NsXCjt1teuad3iE2vomNsAVJolQuOwOq3GFHf22XSLl4M0kI2m3CuoRgtt-tLly7qPvu8muw69ErQrqwLoBWeU3lpdIcAam7z4ucfDL5Q2pqYREk8Gt3kTpINp9B69COjRAi43_CnXqjL-L8QgRE2B2yiSMplPWSMTOkGQHwu9FycKnyXEeQa6YX9dqPJrmilyJNqgin8htC2hZNhKEo2mswqhnces_Sd_I5_cyoG5ZjtvScU=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_ueC0oQv2Dm8xRxkgDQszPP95UjcxznVqfxPl4agrkxFrOhBBhunGJMirwJ9vTKb2isU0XV7zg69V1gZcs5nNsVjyGPXn55d6DRIfU1bK5ePUfr2QBy6-ktwqXUpE0rrSt1ts9GG4IEgfGhy96pWeT27G221hnp_9NKy--TGqC701xP02qB_6Ma3qToyi2BT8c8KDxJxkVpZKYgoNcSWxAGZsyPvtwOPeGJJ_CNbWl5tgEWvDOQAfVn_JDNbPvkK6fQUFFx7-pPxtfw1VuuLXUD05VoTXChRrGtLibfE1ZJZa74Sp_rqvyNmovBhsEXHnYGVlmQKxA_56rNasoNbXpcl6NfEtk7O-EuQTSQGvAOdNkwGzDFW-bxe2wHslVoelTB5pujQcW2ZJ79qV52Ne3Xsy0qp-VYtU9qnDE0vkLCjiMarCuPJZSSGkIbtnx7pGGVJHYfxmEniEKZncNqm8skbIpCBAXXhXqaZURWrd4Y_3DwlxavuuAruVmhy5Frz5DRB0NZdN3xxmu5XhvIWSmHCEUNUll_hoMg_w0LRw4lGfhEflFLMUAyHYSNItVmhswELntnsD9v8l4RknY5CMj0B-qx_BYJTw2_K2DFj4Xx=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_t6HfcFd-FrcGSDLoZhqn14d7QJBmYTrcqbu6v4gfXyL1l05yAqoOFAgzOkfDe6kWISipnoREOLxGwdjIi20h5ydvG7DwPuSFCbKfVH97SlGFqwbN_9fmjJsBJBsSQ4eWle6bnitpftf1oXqCSFzZTC5HmoJSGOlwkePp6Wzii0jFIVGexuGIb-4ocjuxQL5Dpx8hN9oodQP5OetxVlqYFj8xTCynp7KY35Ca6tu0Lr7vfaq1xsn5TBn2ncuKJvSUA_U-_CZdb3TK_wLnx3DQOiYNezk6hqOTHr_IaqNpjAflh9hPi5D204VUY7KfoTtxlm3I5_8kJirHwuDxwHIBseR1_3dSCS-xdGHSZnABdPZIUQimQPEf0IWHQK0ljTqHMjjMRHth5HgA=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_vtJIZj2NrqgPVaBqbZ3oRe333wpMQcOZiXI8bTEGQCIpScwPRVgFmTfByUL7E6l-oUfyQYvluWEk20lTzf3pSw83D_NHCA58R05xUWyQW3fR3fZq6X9gVPL28NMPYVKBpfvzBi9JJt9y6Ga7GsPDElG2pLrWr_PNbm2gh2GZNJM0qI6ePcbSZ_FsADAY1ZP8yzMLjIIS-J9IRQpLJkh3-sCIJHc1FG9Ktsa5R4vzLuT6DtUkL1n31QXzhf71dpBa13JMc7eU7wsF54n8wscv8MT30mO57aMVgltDnbSke7Ump5bquCQ3Cew-q3FD_-l03Z2QbApOPXv7vUAj1xNasA1dKZmF_b85W1fGJt3sWtOx8cKI1HhqNBGwWNxT3oI0Vp8CjVsg=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_sn5AObLBEAShWTWQ2ryWP-rh2LlYhST-4EVk7on9INfw85Gz_O0GwTqKGbNc7v6SO49rxKL6Uy53TUVCn7hS395lKejVvgDjmHyYaqc03Sh3RNFRBLFoe34YoDxCDOGaVXjiGwEA6KApuGFWGA6DuYP-L7tq5SddixQe3PBBDCWwOYfkv0148rK9sxPgukad0MiLaV15TV1Mu7fVqjDaS_XRcdyvW9QIAZVqQxEh4NGttO9_kRwrjzx84wfGzlbohZcQY5qwmW1iix2nVkduNYLSZ6VEjzcErqZlU4OO13IuvFUXAaE9olptYcuLWyNYNSKfK6PjhVZX_ie6J-Usip7ddFCUR_4a-OVMOqZJU=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_vShxlGJxoLo47sZT4DlFfBR0V5pBUTZ709hr70lgOWWfocYpu5tM7TDZFHPpwOOESHNXW_l7isEP9ytaoI7pTF4e5ysbb3bp-Gm8e_z_Xf8SPHnMglFsZoNBBJrvXIItuBFsIwcy0OOKM1Phj0REijVWxIgWCeP3Luq9gEWDaUeLeqFW8MP-kcjpFkvyzflZwFJj4IAC1sr0ecS19V6N5-ZENZT4D2zufbG4DeXGyC4WnU9Q88eHR1slTmGhlfv4p0m25jfpMDfyl-=s0-d)
![\fn_jvn f'(x)=\frac{1}{3\sqrt[3]{x^{2}}}](https://lh3.googleusercontent.com/blogger_img_proxy/AEn0k_tAEpDePuqrmfZct1aEeIAPbFS6EwFrrNEwXuLbF5KgRC8XZZ7gllJJLJFRwNA0ORH9FIujKbT-pBL3yr5Osn5BJF-q-w46A_nBqpzolUj_IeNX9ueWuKgAJRfsg-pWdUfObsPihGY27eqag1sldOtMtUyb1bDXM2bIUUGo-vvLfKFM_SKclWUps8ko=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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