Turunan 3
Contoh 4 :
Turunan pertama dari
![\fn_jvn f(x)=\sqrt[3]{x}](https://lh3.googleusercontent.com/blogger_img_proxy/AEn0k_uzWH0favRDhQ42mSKhhyWFa8wYspAlvk-tG7SCM7f7bmpARt0lGaVzCq7rzj7JyJcDVSM4w2Xf3yMW_Gb_23KO6EiuL4WpRVxQniMoL-ZBTeq2IrsWsCBT2qq9sNqtA7wOxwf9pJdvlKKu4w=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_tfOhRuYQcxV3Liz-fHZuZ5aSnr-PuVUKjOoTu4DR9ojpStlu6-KiVh8uBlBbQZENSwGOsPJrw398SUdWsdPiMmDIIblExjpmNZRLe-LthZgz7xzwLuB-YSixQ0AGMGjJeJqQHFlIRhvAY9Yc1TU8hCQw39ut0VSU9U92R4xnv1VimkuHe3zyfygfPYKnbqZHtFWUjLK6gcOmoy3LYu0VPXNBC9t-2qV9A0nxfSTSYuFVd8WyK4bFp6bpBg1AsJ2KD48SeyAE_VYAVRfbsNLKVn-Kk8fpvx=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_vBuWxG3hRJA_ARM99np9X9uk6Gu9cxjGi9QtRX0tvchEOWqn9fdpSg6ggX-cL9iNnDADPbw0yxraLdgIBepp8uWiP5tqiVDDcdzce19UO3Bvl97arh8b6PoGHdTgHFGhyfhpLd_Of8S7S-xlOu5SJJZMpTmHthBQ2JJAQ9tF1_KgbOAXs0F-7cRUMjkxotDBAq62Qx57nD7DabdWEPqmxg1rDhF4n3eC3uPrrAk8kJj_NCvH678ZeioUBqHNS_C0WXWNYLc1sk6Odom8P7_nyqH5SNYgAKa41uzw9UYmdgcBHGTiOnruYwJa3F6V9YV6dlTtaJ5mVEHTqj1LjKJDZ-zwc0YQdouOay7Xi_6_w9Mr9VxakpV5phMwGKllHDSCeTi0svWwJWV06IOOEZQssDFqQm5YsXx9a058TWq5AxY1lE6ZDgcmIf0Y5aYu8BtkkbXKHgM08fWYNEWxHxX2NRBu-nkzs94fT4zPnWl_A-fQMH_YApjmmPeR2QFrdKJg1QXjeMoxaUnGw3rtJaFUb2ogirmz_-rrTzAWvafcrFkao68cGsVhWpRQR-PjKmM7UlzAm08FFjlHIkJRnUd4JjquXKooHOiJUWKzSdaZso=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_uXfC9kM_fqdaomg0mo2tf5st8ose0nIiJE1c99_wRoekzAlyH0UbPNtaNgnhmb_oZwHCsza1y3CYhiTicpBvyObGTUi9qY3G0Th9X-VnPguGAHTsbuqfnZcA0JHorWPMAUJbhoc8eLPU6luxuHXO_-JRhH9-k4Qrs32e1mb5tZFV-x-4mTRh9fBlgnNs_kNSBD97o0Nu-MgdYflD0d4e7EDeySb1YVRueYQqx6kmFYyseBVOIOvKIW7Y3W1p3re_fl78aWcu3gFWmF5GQFE5MG2mezfOnrm7kGA0XmYA-dRkt1L3sAvlT2c9h5w5clvL3WTGOQQi0hBtCAxwUcJ7tq_dScbWnjrN2RhaDGGhmy71TeRItVSo7mtK7jpPhsi1-dXF-gy6TxhQ=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_t4KexJk8mdszsRRHJALMbGsssn63E8DtoxdYCVlFZ_4a-WKwAXOyqvEO6dbpnPB9ax-RVTTtbbpZaKi4VGiB82M4iOj9Z3WDFjSUQnMa-Vj5xVKW46Qe-jtUpCogFc-sd9gwRUZCN8FwE9vsSfuF3pDoCngpS3XwWaf8SKurJp8XOwXkuoVMnjqQyVrt2jmyWoBfrjXdRH5HdGN4mOppiFeM7G738jhqRSCvD3cyHy0QoAIwqQu5rt8YImWzizUlcBaUvXBZAU5aD80w-t8xrnVbjIQu_BLEG2NIGg8KDU65nHKGBhfe6Kmt0Qg8abIU4PcZ5BjK86fwFgFy_1ZhxW1EOHb5H3sX-mj3_At965Oi-aZb0PpHmer3fHziaFW9gikvPdsg=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_ty8E_hiTz18QxvT5NU4OlPyWCoxi4lgaKr40F7ujF3Bl6S_wNYV7wUlu9Ziap2R5K3x3m3QuFtf1JTqqznpDdS3Itj2sXKZAuRSIJi1yYn7DMVKBZSbStWPtFhB3jEiYSy0zfQ_bsv6qmtTcNs4meLSHQphUl5nUugApZ13iGM_FlnRKTD1WjNs_5m1xFRFUWmX4Dp-Tk6d4YGL2aH3QyRVJ9NIu10r50NAaiDM-4x5T37H3Z0dlghTm328Csns3Pn0VKlyukH0s3y=s0-d)
![\fn_jvn f'(x)=\frac{1}{3\sqrt[3]{x^{2}}}](https://lh3.googleusercontent.com/blogger_img_proxy/AEn0k_umfvU_6RHWsWH6V7wBptIyucBZ-zjGfIYDVJs35rYXbV6402xpJCTf1Mc-AQh_-stUyi2PyTPwKGrBhhb4bSCzV9fXURWmkRRaUhPiDoz_3Ram2QC2AqkGl__QuOel0a27czPX_3AhQr3zifoDD6KPZanS3fwEGqn96cKdbPmdTH1qcbQQQQ2Z9t2l=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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