Turunan 3
Contoh 4 :
Turunan pertama dari
![\fn_jvn f(x)=\sqrt[3]{x}](https://lh3.googleusercontent.com/blogger_img_proxy/AEn0k_tIjhUOVRIhw6xWzkjsNGcQ2-etph6rqDga_s5NhRNYRCQ6CuIcx5UZeBfApA91Eki9C0F6tuH7sx6NIOF1xBZ_bUaiOGOuqyEgtcemcNIrcZM3fcRFYi6uIBrMFDTMj2m5K7x7GdkntFm-yA=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_tRqKfv1cR4mgvduVOGT0aGilc03T-eAL1j-kZIdnkhoxqhpGgpW38AYrxSkKFZ4nzFLa2y0u3qssGUEy3eK6nhxbltlyzc40ZAHse_7u8jbcsAL54SkAnY1pupoePct3NbZFmj4U04Ws6CJ6a8ff-6HqSW2xBKKg_5Ja1CsGReZOOVAfzfGi2yNBGg1DZDsSD-0MvRoFdx6GhSSrU59pN88MECVhOxjMIrymgqthAFlC09r-LAsuZgdnBGx6C2GXMy52yhyZJyS8sxLid7wilvgPO1S40S=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_vkkQTVTMYBmy8Z0TacTRbPomCJ8N1rq9sK6-TzOQZMm9HV-OFNWieAUd73MHYjNDXDqzaY-y8nZZ5CciiZ1u8XeEX0MODffhFdgzIW6QqHBfqVRNxW_QZJsTaKJugKy-Pb5CcW09sMlu4VCl_1HnY0BX4BCHWOm5j3dc_XzevjQBsGmNLqlN16vtlKHfMEUcODw5yN4hor0b6RGnnoWNVWQ1_40KCL32lPD76A1jMTaFrmwZeyzSF_-f2UpmMsvEZhX2v0zSFbv8MP0uJa30eI3bqUtWOtj2-Xj4EOktLTeAr8IQa_mUfha-LDh3sQHkiLF8NI5hdts8r2uw_ofe6-sJsPqr1Z_hkhvtSGzzQalEW6f4QPhm9Rr1wTRV5bFvN6KfdSF7lci3GERb7rZoYVyzpn4lNz6jnuee-qG9jKq_e42WWA6N4y_Ed-2VjZ5vge132xjIVd1If3kYKK1ZbVTzv43MfRMMoaNUoVWmNxq-85TsqYXYk3XhOT3cqc2sb7m1Q_ngxBM414aWFq_MRC2vsmnF9vNhC2kVBYivelmhSpT2Aw4H1_iKnzSr-_OykgJiDjMZVrnQqpZmtLPnAy6G1YiOfofc_gtqXNSyNY=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_tjt3-Ud9J8JWBZMulw956uzhEzjuIftxhv7hPIZNShTiiKLLhtSlMTmyUFPxQCt4iGxtiyVpR26PEPJrcI_RbKqdYE6RQxuV-EPzW07KC18vGvMLhSErlVCI0FLLCMs_lHIetXYskQeVvSVptNwZgWYAaYKVPwbc_1QuZQpFLcog_eqeWfvF478lcFo1t9B37Kw8rwPe49s6ZBxqJWPvxD6f8aTaf5IT2W9xhHmnBahyVjB_zwNrdayIBuv1D7UaoO519QKPNJ35p0o7BIITMkzyuMMzF9VXlW7RUxLWkLrkg3yYZ2MfjFuGGEihJMBB7KH4pBXvSybh906Gywmqx9MYM_1eoUv3mlK3T3-7-ZM0vlY-7Jrpi_z6tCaNbADeHHIZUE6p1YFg=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_v4SKK7ZFLs9_WRyVGV2Vg1dhdcV-fNl9q16JtVgGlDN-FUG18A6poGWtzR77m4A7CyyNtzYN0mm13kdMLjc_Hv32F2tCiAvD45wN4TG58yTc3ddFlhcB5I5zTkkcsblB-VDx-Qo1US3esIKcqpoGG76ZnxtdnD-u16QvMRG3JGY8oip1Fb6ga7cvRk2FH6vYR9YTEdGFi3bYjdDOfXubxn9iJBNhwUd4HaTznbFU3IWRXusUDW0rFcl_2G7o6qY_wMeI9Yi8w7dykqWKQAdEPyxXO3XObI5-h3-dlIUfIyjjHrk9OgGfgXuS94aim9H3il_RnO-UFa9_crmvRW5V5THCZW7LPDSsrb64DlKxRzaPoR7ixk_5YcLst90btkvHzI0OvfUg=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_vg5vP6i1_Mh_PRT_RBU_p8iyyKseX2eYQcIIgaYZIaERqppmar5IsfNxzQl43D_vY9OfOvTJEr2jlO9cjBgkDmqaqHchPyLa-tOm0sYl7XoT2ANp8KoADJN8YKFXYOvIOD6nLgDVwBjew_3xaGRLR2zpCn7NxyMuOIxnodUhcWambrFUITkYokeIbvtO2B1VRkGNxO_wyjeyIrWtiJJss87_c3uzstnm1VuGtyrKBCJtWyWL_pwj6ablKzYLwIlLdJP-TqKaAfC2jGA7xl0RYsh5I-CqnL4yipQ_DZ_dPIulESpRCxq2XA9B7BG21OXyka-FqRpg-Cj4SQvqnunogEV1pxCWyUf-w3gfiu084=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_v4xkFJzOapPkoc-FVM2E2mH5DdeImvygkkr7njwn24-4mbzuW6lqgDiZ3akikCnVAIbQR6YFt-9bigbrcBNdLxXs8gmrDzQWPTFEmu2rj-fwMN7xLKO6951dSfBLAg3WHm4zrBja9ZilM730AwFpLE629X_sce7-JGLDA_Fd4qStTfajh_VpuFFNa_GLA6KKiLVLuXFJ0kgijboZPgaXidixCErp5HXU8c24iaxYP0AH6od1SQT_yorLycV6lzbvOUyBo5mCA8T6Ak=s0-d)
![\fn_jvn f'(x)=\frac{1}{3\sqrt[3]{x^{2}}}](https://lh3.googleusercontent.com/blogger_img_proxy/AEn0k_tpU-xzBGFYLaM0k0b081eyidGzfrerzdXtHg5eZURwgRO65f1MK0pESP3blgXrf5IpewsRn_DOimkFzDNSw886S30yEGe9SXfUFMwsKcaGiJCSbkV5B_WldhTupnm0V7b1KOQoPOo6LA2j-OivGu0J3QOfrk554K663OqiQxZwtvA6W_Hk-VwhNRdX=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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