Turunan 3
Contoh 4 :
Turunan pertama dari
![\fn_jvn f(x)=\sqrt[3]{x}](https://lh3.googleusercontent.com/blogger_img_proxy/AEn0k_uQpnP9ERqL7O2RQ-2_FZKuXElGj0gZvtDxBaqIY_N08q1DqrHPsPTrb9YpRIVmaHorZxFzv7DZsD2tAXCff7JQptuOHg9R8f3Iky1CXe2HuTF0luzo_VB5F43NagESjUUq7tgNv2Ib4V_LWA=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_tNMPLVMkMJ1TsZm1VnTpoVZbpy5kYpeDL-0C-QnCjf3_TGcp7yH8uWRZdw7F7iAqKoS31imS3B5-rTG_WVj1plelMa0uycMG5TRzhtKvRqT-aLGv_xQ9wMUjjICnLTVCQpg9YQBAFLY_vdAjnFUYZpnUQLrs0bSNDRZf6ZKKiKJQxeapPBDQTo2VueIucd5MaPH0fMx1EGAQJf_l95ADgEHPBW8KKB9LSGpgsabK2KtvF20KJATiUV-7WoWcUB4X_9iu693tZ7amoZSSGRe4GXE6kadKl-=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_tS28MEe359AyKd3VVkuIGH5yjIKoIA9U_hH-JDOmV5fN4IlE05wxYluBromFHuj56lltQ3I22t68UT4bMEFRMIDSovrHfX6EsSqFkOAAYHX5witt8UAGwnvwBQXXf46Gej83uvd-WAfCDZTjfW29MCDwCuBpvO0G4ada0DCd73QMqHnDfhtJDkltww1Rqwv9M0b0kYtrL6DXoYJQ6hI3TMIZ0emCteGpS3zj5dzCHfqfW21j2nvN2iH2Dlo-5WZQezKWpJvhYLp7fUHTBOevMRH9XfoCqZZTw3LIe6zqoVYhztp8byCwYcFWABSvhHgG0cHOFOSb3J7MQcEG5fUTXavCFVFQGfB0EZwrD7xyTI2vUuTmVPfHe_-mRvSD0bPEKrfbhSVdGd_NSU7hdrK5TkpKliPL8ViRzjM2srRBoxvYINQ0O5NPFYx356mBN3KeZc0qB0s9TvUGKZw56BOV4XwfPlJxpZTmXdDVIkFJvPHhE1xgwRQ5mZo3Df9megRlX6mRXsCGbUnlj8BQAwHbYsDJo4y1pTjostIl1vosBj9OXXHdzoMY8ByzQWafzXJj1LCkuFqFilzn3RhRCxD8tLWwYm8DDsNRSUnp1l2i6Q=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_vGL4zl4J-NUCm2RMAKyE_3fO92m_Yh8O491bohIivFu8oCtO_Nc1hR9JnBD6z85HhWtWk1qJfEu9M7Ot-Yh29ExZSCXnRi5ylt52be6lPA_d0DZxmIMilDLaTB9YfWRTGhtwN25gOo--7Uu4Q0mzD8qtCU9vrPEUQRNmWF_j0OythspLsQ29GZY-xmCRlmvpSdU0VOEUG_QQgjC02UVO7OaYyOOfjwEIfU3IEvCgdgRmBli6aM2s_3jGo1OWSIbyDo9RsEdTmB5mKz9NHbgABDpc1J3sf7UgJJa5_X4L-vbh30VxpvRA916LYjpz_BRQa14qa9GvzPOdrY5pptAURW01rJCVMQpWoQygL_bnpDoFKgYtxs-dxHnyYL7_wtD4P5Eba6iuRK9Q=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_sXowrL2O3YrTbMVCydY6uedzUR94xgkV3VwDI-xXeQ6b-d4uMwBQWiBQp5DWicWga1kh5DENzSpqtqyRzoJB4HPNqyeQOrf1sHzzXzpaXeQ_5eTjOh6roD_Rd6ZioNDdilt5NbY-wm9hRB2yCPzRl8tgGcXDYuAd-X5Ux4c4WJKtbQLUIE-9QGQxhBhPVCkWcs9w15EcsYLrFlXsTh_azL4kfbpGl9U6ubaIIqYr33KUP5evkDiIUhAnYcZ7t2QviFWiRDIlUauepUvNSHm1jfPyJyNZzbqwrYEnSllMWFPpf-Ru0ozbBhoZChkw-JupjQOVhyokJKTo9qi0hpXigl9MEWlu1o5x_2d-cffeKslQIWk1bF4TnqbmJfaE-yDJ8E2SV7Cw=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_sb_TmiGycboNCSyWoHdXmCCiqVkZHnCMMq-3L7MWn9WhNSzZHoX2LqSyco3dkdcxF6uA8WZdQhP7J2vL_TF4GsH6sBUAQyTypW7K77-JZNtggiH2R27wli8gx3z79fbFnPhucfgg6kzKpz5A-Pv-u67ZUCxlTv4BJ4rg7Ei_ojFTQgxvIgHV2i4kQLP9vg5Ldet-UGPZBc5Rk1JxJXlwaaNIupupfTh7m71Dn1lIrvtlJpQ3k-PIhIloJJF4yVcBHlu9x4HW4dgW0G1sOY66E-ijFYapbVXoP1K5yEcVzk3wguWPiEAFYPpBa880VMTHtMDyqnMedAmpgihSzqaNp0KyenirgzqueS6eC3OSY=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_vbRM9KSuyDc1zsj1fJWwgHR9cu6QMD5UDscP9DcdhRhvWYqbHJU9Uq6l62AtUcfFKW7jgHzNdVe53IvrERqQs6oLwGTPPGjVHI_85QmHizczHc7QbGeef52wqoi8NK-htarTY4t_zFx4MiDa_SV30wWutHS8kVwVXQ8rGi307lYXtWZtH6ygA-c7YS4X0jsLy3IlnrXLfO_ShBPo1AOmXKSwhanB-rL32VQLW9HMy-GLn8PxWDA7CcsfaBzhq88QQIp77mi1xFMZAR=s0-d)
![\fn_jvn f'(x)=\frac{1}{3\sqrt[3]{x^{2}}}](https://lh3.googleusercontent.com/blogger_img_proxy/AEn0k_tqyFFyQPWA6vf4K7Z8LpHUW1eP9MvtFN-zQ4n4mvh7c9wGBSo-in2HR4j2gC7DKUzY53UZSs87qAXMFC55flozuOpldr_BwfGkW3pcbajM6ZE0lIhnDwCNsl75dgOEjsrNVDYKemlk7QbiJtUV8yQqfsNxnqUP47lWz7LvlRBIKnyKFjTkBiUn9bnO=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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