Turunan 3
Contoh 4 :
Turunan pertama dari
![\fn_jvn f(x)=\sqrt[3]{x}](https://lh3.googleusercontent.com/blogger_img_proxy/AEn0k_vscx0OybkBCXSA7FRSfa_gBhsdW93IXRjez2v1r2JXp6Mt_ciuARLGT0Z2ADSbq3sFqU1x5GatPZelNJfjYn30b6XlQEFFA7sPxCtvhRg0FCi64mdyAnn54k9cG_VFVzHyeNAkjJus8ZFyUA=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_u-1ub_SiljufjEAWJHAu5eLXWZfghZZNGRlFFxsV_j22SI0LXutMo-fwuKYzwj3LwsDVulu04I-ivf4VFnSg0asZIo7lt71Pat3WSAQFY5QakDt7-2B-TlEr7Qc_YOpiCfpwdvL2SWZ5t5T8V8JikNUHR-VZ86Tiq5jr2PIBAOYRQoEjQoQmgfC9GGKoQ08s-62s3Jq_6ApvON30mF9O5o-RURuge6uVF_MBQQ7aee73lltOXaAVewJpyJy-fDvTUfxCkrgKjdZylujBUsMEs4MXF6O7fK=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_s8pp1pqnvmq37KLA8nbWj8WOjiaj7r1RzxH8Velarf7Hu1RmjfJ1ZGdTk7uKuu0_HMEpq40PTPnpiGYJs_X1ZYbuRvrKNXj1ETNK6cWSi9ucl0kSKKdUsYPvYFdL88w61VKTy-1CzTdwZOSXZFZmy8StArVl04MW7vibSae4bvljiwXVhDI116Wl13dOwlsPvtCf8DbwnVxCU2Kq-hRN1IicERmxuJR689NfH1xgUxPvQPjqLXnB7eRH4x2xIrrlWR2AkBv5wUOsE-fUaB_omukzVZrZ73fY8rk4s-dnAGgrNS29mM0ZFL_vbe4tLfRmJNS33dj96-frR5CQFA4P-9-192Bavb4RFFKJ_yPSP6U_GbHzgu6PQ1shlLaKLZ0vj2R5KnshvCuC5oeazyw5y9_U-fAvZDIXQFtH8CzEVDj2ETseNASIsgtk2XNeWm4aCtR9RoxNQdM6GcLd2q2b74M_7R2Cr68BfhuTOrPYfnyX1VSIiTgizPskJqJy1fTViaoSIQADkf1fDp_trYD3fmnKVibStzni2KTq2qGSDF5RNasYCkGmj-466R2yktA4_hVa24MFXm4usRpcXAECOC9roIkLvSAF6RFJ_9qq9a=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_v0aznBzw-7NSYAADSa7fb0OIX0sw45aOedANCtiackSY0U7WsHk2ZZlwytsvt6XwYmmy5riW5ygAFgc7KJrGRn1PRL3N-I6sruoRapH2tPqHW3gateTr-tEMBdQCzMNrWAXUcYNBcp1KVXJUKwynfvgmBgcsHThdW2qGJWM0Ynyo2Mfx_VWFqbDO8rohUbGDoe2Qu1lZeE0BBrUh-dC3c6Z_SbCK9c9MLYaQT6ztxjlWn_gJwqPoDTrZjOeWLcN6KR8n02itMcJh0TU90L5ME2ZK2oarMHCdCzRJUHy3KH4s-iJbXrZAZdEcd1NDdIrQSYvZtz0b_CKrZ_gmYMAsAUoKRMqxPGh7yURDH51_WifA2bL8dlNCLjdk7FLqbVwmYzDYwERnk3dQ=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_utrE5FC7nE1m5tMMN2DsS69U6GnX2w8ARscv49L8CtH8VocwdJCRVhc0P8iKn-wPlmVVq2dslyCeT_e8o9qAM6ylhHIjwcjsoA1ZTgSQAyDNjog731aQXpbYljMNeKae0hh-uVWjWYJAb_SKGLEguBxsVuvwwD3ExSxhYw4EkPLGMrd_rEk-iLIvlO9EgPx8dOG1y2gW9TBzU1dXGMPtRFp_GrAjeLtIDIUuFUl2zLLfjbgjI18OihQgnyzE3t4aqFog3317v1W9cJ-BR_nwbYrSmihdjVldSxyhjGSd-1hqXMuJF-uWXYeoBXU_21cK-m3dRWjyYE9wbMZCfgTm6o9lGra0vWQPtgxBY0-mEn2irkI4tKgjp88-nTs-YABP5_WNXcgg=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_sEwzeQxSOz3towv536x6nIdPJ01hJvA9cAcmeYOzZ730ptxx9xzLNg72NvumRmWbJsfQfdtYJD9cZPzd21W7X6ZE8WOBzYetPUQRijjaNJ8MNIQwSZwolvdcqZXd7GVwhibHrY19cD9CqgoAnQZ0tOwqAQYRU49fVPErcp9dHDyt4Xdgo7kPiM34U9mZ8BLm3IL0h42bcGDViSmsEeXPefqvJnbIy2rYMNc5So0BF0l5PHozha8iGo3yH3Hj623BGPn0WpXIy7wUeg0BeHPlUipUlUMRTKI3gyDRM529bs1xPlGEd4p0Hea5Ek8awhuLfBzb3vXd9Jk6Hxgp4EIz4lO-AxYZvxUiJ1hvXKW2k=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_sEdM_hEr6otzEAhIudsDmZQc0psNYVlAhoAJYM2edsJG_VDy0CO3P0Ch_QEYOMCCClLLs0AL5RyShRPxUM6iCdHJmb17NZzFpKc-EMzzszMpE9gE7880at-uVqYMi4C8gh7uAD6SWu6BfXL2kCq0LULu1qgyi0RY1pxIlM4CfQcveydyo6vwJVmKwMo7__jdqdIzW5oD5gCdbloiSZGQ2OsBg3Tauqqz_P_a397fvGFcvZvWStTqblBORjLBFwowOrnweGp23vxfQY=s0-d)
![\fn_jvn f'(x)=\frac{1}{3\sqrt[3]{x^{2}}}](https://lh3.googleusercontent.com/blogger_img_proxy/AEn0k_vIT_4_Phx2c2KN5fGGaYdpi9aaRax5U1IRexEFji6O4_Bdu9X3p5KsH6yblWGlA1KbQtRJJkbc4Y57q1gAoTS3Wh7K7WUZvEs2K2aeCkaq-hO8ME3UaUVhGdJElRktF6XCrI9D8PvqL9wmd7-QqrG68rIIe1SutRSGAAaz7dVie64SICfCGJoYdI-E=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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