Turunan 3
Contoh 4 :
Turunan pertama dari
![\fn_jvn f(x)=\sqrt[3]{x}](https://lh3.googleusercontent.com/blogger_img_proxy/AEn0k_t2Od4UuV-dFqT_xaDr3oVTrFr28PC1yRXgiUwbL5tMVLtL2MHQuvVC0YECtDfc_k7dKDNWFADmIcIBbnxjIGNm5qq1_xTABBX5LSa3iN1fG1ii-epS4qKnw6UgMxeIu3cYe_LlsvSOzEoMrg=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_sm3bgpnaABDlmo4ulRpav-V3q-uMPYTBaq-AOshZvjhmi6PMGNGPD35E08uI6I0bq5N3Zdl3ueaQqPr2D_Bk6kve5KFmHtBF-1uelvPCAzySUySwvjHE3baKFL9uke4qx1_naX1MhHUHWGYfJnWJlPpFfLH2d5j6PcsbFLIWeb_87G46udtlw6-eRHuLuxIhUBi5Y_q7nN1VBTxehT2hqJwdsWOcHfTUz_vzM32uDBV6LL4a3E30JKkX_8o6cChDPchSnKsEzyZWzavPzYumwyFrxIxC9J=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_tsi36z3SCv59MIeu9kpq85D5yoRbHqyo0_ofmVb3rVwDBGwsXMTlR5wN9xEWr-p0fMuJBrSyNguYZHnvugtcFIzz6arW0O0yd8OpZHFRRJUW7Os8Pe7wt-We-TFn9cFMKDkiLmgne7oQk1NF2bFNp53Lsedrt6w4OLkOtMYJ7QvtI9xoNgZHC2ODTcVqKD01hvD-emmuzZXfWs2c9IxE4MEZfOatzS8nVGOGA_JfvzLDO6X3KgvmQYGTXhh6NFAZjgqxfV5bEMuHk2Y_LkGnJAzjk4rxg68Hj_m-u1WfnFWRP5mRXCXkG3D_uEGW-DLHjyfFiRw0PztFZKuZteSDbFJMwForxIqYsWdeiLEBrphyOKYzcAYHR6cHe1ImfUiQ8isQpM6htoJSs94PxypeQX_95PErVxTCeOZehY9UDrORMozuiWr87Y34CxUISYiARISLEgz9kncZ9wxwdPZll2AVby6zWsfGrHWmJuJBlXwq_5rpZpDbgGqG3A8moRT-u1jubrsyh56IGXFsvX-TA93d0cf6OkyziCEQiG4wrKC0i2Zxft2gcrpcOK2bAyX41h5E8gdHUWSlhXCSAK_yzmffCj3683eXXjOrNz4Xod=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_tdwAX6MwYD1VFf2cRPzSGeovVzmZ6Uz3sQW5sp1EsiDTp4_jYVzHDPbZphMHMYLY0MSWpO-urT0QWVXVq2aTzcs32sngaizdkDOFh6anCh_mFgAvpshw_DLBuY2Y2bTs_A9HMIgCFPel3Nt71vRZ__0l_ZZAbrssF826K259n_JAr4rpFOxxRmhMkaZv-UWPD-_XtVq-4Z4Hj920oQJGGGXtml86W-2KwKBPQsE6OmuA_sHGkmh3nOjXGgoWHJoDV9h-ccQXD16q6a8bY4Vh_0sr4K8hNy9ukIF-4jpOvL8NFLFc_gZzB9g0jHmer23pXGgzv1jYmQwsiDW-KOIt4oPHks3GD9YYYzN1ebmh7qYU6YpmvHy-J4oGhldi9vzWv7ZE_BG5bCYA=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_sjKSHsWuKQ8tpSNWJOjpCOahvt7Q9P2pMzeD4FiG3RWcPRKjRDlyJeRnfnLzgrlVFv47XWGoMn3Rz00iT6La1zccPOxUMHJm7U6bdj03nwohBi-IwG16SBnrwjnVHC1njGNSKVG2hfGoDO1_HiuBCWuwdsr7qLDC604JetUmajL0GSrQtKKfxgexjRecbG5tE8RLBVfj-N3YzNfK-7QYdbUzuGNmyR3zTVbOtk_S6mcgNfohOLCGtwA4D_Pm54qI6jxNS7qQvi4Pn_0XOCbqCBjfmMkFAzOdlkcJK3KqXtIL_4cIz-DZv3Ebg2fxsPfDNRzNVtYEPcNAOcJWp6ncEpAxZuLXVuVO7pMAi-_sh0s9ltLUVFxQblaABPyHvtXlcYtb3fgg=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_tlkTC0lCB6lfLfIgx1HG2mFBriGxgJuslBod4m3qV6nIiA41ECI4kxp_Ylb-Zc29ti_4gMsIoNnK36iWElae826SA4nDWZmZly72b8m4h0wd2Ba5Lw4UFvkc3SsQagRHczhX_YoCf1du-hLKoxW_4cvfCnCOHNfsOEzuAplQuy4PYYFQbcz5beYbrwuadS5bZAgmivriQee5xhmxbTn8Rzh9cH-QI--LQViigZGCH2vkMBUTebqvlgedsjI7RNaPufacX4DZe_UP9n5cHmBmu_4Up1Bn0oE10mVUyOeoHSJmOE_MiEqTJO1pmOITS1tQPvQ6vKXHllFQYD9cMgu2OZemYewyT59OYHoUvbH1k=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_u8Ce5-h3ybzDyrxsHIgfs21s_2n4x_bL5uw6ikAWzbh7h9e8e2jx0XgoE6rKG0oXYnNoTKp7y7po09KWsaXB_UYSkNIFVDLkqnqzmTzwG9z2-XXgUJitABCRYz3DcMbnlnurcF5npYcihBrv6KJHDoiFfmE-8SnAqbcjyfHEbDcrSt1c7_dhTUE5KK7BfTPVlvtJo40Bf-ZochRWNRP0by3T4YE6zfaj4nHTxNILZGbt-7lj9pAGwkEvnrp50jbP8W52JcIkOl6VpI=s0-d)
![\fn_jvn f'(x)=\frac{1}{3\sqrt[3]{x^{2}}}](https://lh3.googleusercontent.com/blogger_img_proxy/AEn0k_u88GdPrOPNUjHA-YYAFq5Jdb1WeWpl98HCUd-1PHpREuTKKQJXh3wChjU-q2V3SbYhZRljEEEOXRW3klyU4klls0082PdUbXBFWQgGfHcgk304fL892W1aNohVnPaL-v30HIQ2PZCb-75wudi_ALokeGw_xISopMB9qfo5RMRmCbC2TZcLIUbdcV-F=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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