Turunan 3
Contoh 4 :
Turunan pertama dari
![\fn_jvn f(x)=\sqrt[3]{x}](https://lh3.googleusercontent.com/blogger_img_proxy/AEn0k_vTekPq-Bmmixk8fZWLzc2P0CDuSQRtRpyggiY2qEff04OsP7CelnI-04nYgROo55j243CpsA7yoO9cfmJEXTE4oqjE_vmoavsb9ggfETU4WJMFXqlWWS23A8GRMMsX6203cenPYIiTtOlM8w=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_vyTjazSl9bBxzELLQgbQhKZsBYiTJAgs9dQmt4QmvzcJlGw80NNJSv1lNNMamE10-KW_6my8CRdVYuMIq9J0xtpTaSaBnZ5RS3TgyTwg8X4VIw3e_gOjV_uRzB3t8YIoaYaNdAOrRkGC_94h-BKefX5AsyynEXGJ_7DYdh1N04Jg6z5zbNq_ijNWvQypVcHA1Glpybu_hKHi_qkJuJNAL7nN-5QOEAIFr1GqxpH3Stbr_cfbdnl-4QvzPP-Fyie65Awjfd4IBI743k7QLLQLvF6pvWMHPT=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_sb4ViZA9PlbO-uJW-QNUzw2jJpvz3q2PqeHW1JQdWLEFnlb0rqFiPBAYHqk75m2Fck2Gz8NL6dxRoMIkGGInZEE36QIEuKDR1LbbcWYYc0JAXfg6_xn-7WZWt8jVWsqE1ZUhJdE6U2VeUZJQfpEWb1c-w2Lp1iEDEzxQjExwktI__Awzm_mwMaOf5ShP6p7w3HyQ-GXJ-Ux7CjcnvvntcFv_89cW4hNiq1qXG-3GfZ9Geyerp6-tXwapOoU6GSplBjIkzv6L52WYZe3DH1ulz9Zrqa6TFPHto2d6LmHq0JQFR_Kh0ijdEPA_gt_-QDl2Q29SoxIrfA8lFa1MJB5-BqOQP_Ez2uO52mB4uy4emgUbT_RMz08zjxo0Vhxu0PX3lJwZyVYJ0LxhWjpE6igqT5J_1FchAQmxxXWWlL86AYpYhxxy_mLLv7hjL1uoNO1lVN5aHzgTZ80n1CTrBd911k1zG9ZXyr_BZtgQsF7Sx0zQ8-VKw-6I9xnWC-J6ToA1BROhs4Dvo_JH55YUg8q9ga39SPVHeyHY9nopUAJn7SL2gur8EAbpC-GsUbMdOSoWck7tkMFPQ8EYm4SOtnFsfbGuj-_iQmnGCmPpx_xuhB=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_u5ZHiDTt2HZwi9OIyw2ZQUnWm8mN0bFPh5D1pVyfd31pMoe6spaYDJjRTbwiw6HE_RkUZfO660XiPwR5HlXDJ0cz5o3Y71117oRBS9SDSQYCIQtC9TMZfeA9Qm2JncOQiWUFzls7LwfP2CvOktw3twXWMeugEMQNCi7VRQ2jwpM32ILM7UPLCiud8-f-zYHj9Uvu3_aKQSISneBAtw7kt_EPLZg31yNO0to0IXi4a-DNUe9jUyaZ5PIBOdFIHt0fqvnPWENAxyo1XeULYDmNZvL4EPHHFVYA2sXguAbmLkDR2vRyZBf5oVAgBIzbdmTqJpMbmpZNLIn_ztzoR6KHfs0Av828LDFS_8q25MJ08oDoJSlnSTKF1PW27uheSS9mqohXrr6vwroA=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_srDhMOGGP-VKjL8yqWyCvIB_rgxceFxoaE9wCYnHSClx62DCxioRjV0uQ3UHMP24dOVS2ZchUtqNc5HoshspvVB-aC1KJfvoiwE2rKeZS1Sm_EEffgiSlIl6x-NVX0U0KCZ03BBG7aw08kDZqx45bmxNbue4GMZq6t8_V24znddPYfXJhq9dBY-R9rqsLJLzBB43uA1mzoZv0MIY9hJOl24SCe4lX6K2MovEkseLgzunRlbD-IoEmVroQhwgVmzEg0wnjZ0Hc61GRLMnbiWVoOQmaWpPO9TBGeSsw_dMBMIFawMV6jUTyrswQ7wYNREFHMNFmynvyxcb36rrpCb1jQI6Qpy-j9J-N5oZNXVENR9C957zB072G3TjeVcxOMYAgNYZSZ8A=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_uJbNxoylRmPL4li1h0V7CspaICJN0rLxbK_mThjXu68J4Js_6RqrkHMyw9MI2Zz6Q9uq-nyBz4QUyymADHPNJJu4Q0Xhc7BBEcyuU8qSheVB_yMBwRPWQ9AN7tBJCXUhtoT-cL-Xc99ZneU6AvBFBO3Yi9TdBwe7y3IieqH4ResfYkSs3eL6WuKsvTd5ZPaZBoAOSzkg15c6asNEXipjGHTBQOu5KuFdthbl4WvVXKFWAGVoOwJULBDj8WCRPfgx0gTKHHUDEseoh-BdSK2d5m5o_Lbh4iNbKSbkhmHL2040Q_3UnZb_0bfgXKGujHcOK2WpWAdxTgpcrcPTsmBF0lGyg00qji5mx9eR8WbPU=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_suv4t74fhuZ7f2Cr0xdxT4NPYtnyZx2WB4uNmu8TLCXlwKPk2-1myYeQxbz1vd9-DDjEv8paLyrEBRuS2ELUcUaXeEC-YqJUoxYa0LMM2Ghbmo3DjVH2_ftQ0h5pvNnLq49wxeURh_pjZ3dhsIQWl0hDlzjqBk6XV-MTmag-JXNo3LKfW0UoW8_QGbj04IT0zezlykCCl_onNBF2NOfzOWC5ERH3tA7-QPekNrBY1xKN8FRyq_a6mMfO0JWgQKvpGjkJtzKZrWObEm=s0-d)
![\fn_jvn f'(x)=\frac{1}{3\sqrt[3]{x^{2}}}](https://lh3.googleusercontent.com/blogger_img_proxy/AEn0k_vOQp6JaQls7vBLS6hn76CIoUWNNeRDlWPl5AFFs3ojAOiDAuVVLcINrGTKMn7YS0vXYSYORoJfQc1Wk5ErMZYEhztCDSH6LGz79_-0JqvSAQYWkeyH61VYUcCvTJEcGC92fMl6mnbkXVlvMuI06BR6_spQRwYxgFf8m_G4HINcK5Z_0r9myvfkCDbL=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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