Turunan 3
Contoh 4 :
Turunan pertama dari
![\fn_jvn f(x)=\sqrt[3]{x}](https://lh3.googleusercontent.com/blogger_img_proxy/AEn0k_vAbtWUvb9t4hryzABMScUkQbK5AReeH3jJVZbuHKBm8n-s9dN6dXuJ4Snp5stU7-e0tIT0BD-4c0odlUGJ3BtUOH71Rtwh3s02nMDiEULEzf1e08guzWXrjxwc5W9mW9EgNiRSVRVOp50Mxw=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_udSynTT_iTLsUZwdWbHfa_SQZHkJzVMxV7iY3RoFtCHU3N27u62cDpRiIjnYoKtsQBzLH--rloXFWzrI1dH-LEmTQHBZHshpXVTHxaEESi3K1-b-G3S5eB1MT2IfyJBku_xHLBEhhBv6akGsSBhjun6Ps1j7eN7Ckj3jwwqXjNhl-z21W1hoIgr8WMSHjYxKMAF3dWd8J1R6aPZZKjMNl9tHE6X5qtNWHxXLpCwTdwGTNJGJaywWpsEjE7nQEZLMOloGGofQ-2WrT_R4yTbzWgXXDYybpp=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_tX3q5cH4qBmFY17QqmZofwBgxL60dkIPJCPYF1hYFbn3m1NGFi0RxI_gE5jWynnNyn5-JYRr3BaAdK8eW-6_NfxC4vrlkwE37jV2GFq9Q2x7EWED3AzwFVY6vHn9TxxJpyI531m7xXV181PAkhwm3S_gmYi7nsRoJ1QviIy9FEgZDdc7am0r1BpNMHnIEJuKPXhDRuW6K-Pe47XrJ4tO53gU4SPPT9ASrcYmPxao426stUNffR1f8uaWhO3e8u5OFGFjbomFUywLeh9dylpPqUCLQ98rPfMUg9-ngOSk2-RGRWm8TvXemNH9LEbgu1h2tvzMgybPJ2aW3mFhXHQXwM6OKo89jlTMAMsg87e8gho6bmixvcsSI419ZJK9b1VqSM63HfQwjyMGm0UhuMuY2HxCM4xpJEsE-Lp1lA1GHpdCxCjoFQxybddMS1n_ZLca_NwowyRfgXGdqjMogMmzVOQqZC5b64TtylaonUQvdVm1A-CkAXEBMd7_eRd5Qtt7sdlTKwUlE1uMoT21mg6ltTZVTkHjLhBkhiesW4Eavus2CpDnuHYLQA2NkDlsOU9NVYDleRygOQKVMhiwwQzOB69qyuz-dEs9BD5TVe-lWW=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_tI8IbfL0kSb5FwlNws4suJ1URANZnqvfdQr6cj7qOCJ7qGoEX6bH3tcDdnbl1bl7Ij5o_n5MGrfC0EugUSlfmWHnqnNSmcTYUc7RoO4qoc0cGky_xHj_dfgpqE6Wizf9sp4TOW4bCf1CgyJkpfK6ardbB7JkHFVx1vQ_eHXiJ1v_Pcy9-w2f4lC0_QjKkqYtwdduz6y3kRNktU7KjXTR-QybXEjE19eAgtR5wU7oPBeDiw3dxne3JDMu3myEuH4i7EbA8GD8scHUmlqfFFkKiDsIOqnu32kmV5hS4czXpcjA5bH0-aNH9E9ux5yBmZ3KOpp737OLqryKU-BvIBiJsxaM4686qJd05Ib1s6xC5zDEheW1JOm1aW_W5jXHHfByN2GxXdloJX7w=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_tCt9g6B-yZO4g4i3_OeRAmAGhLQx3AesrzT7nF-F6iahtRbFeDiAy2tAn-KsTbzmksSpX8yGGAeMAjaR018hCCSvN_53S-viQZrX90pwGrWh1uXAPgJileA1DotRWdULPsZIiirNoBYYVughWiqx6F84Xn8-R-67nHxmK0q5uh8gL4eYWwJMmrr69GR7QUGEhaMeKcHzQ38d38lmXZ-sXSQRsNSWG5JaUq_a_wKVnts10-MF6wPpCEpjrjdX6aX2FA2wD1PZcsUjxAXsUPZZ0QCfFBCrCoqmr1tnayP4dgWoYoUw7ijB3z9mdtNpXgQr9TRNPQsHAKa177Z6pSk7FEaybWd3qz-KKJ2jDZUJGmoIq5ALfpVWhFDUOajS_Lhnj1n7NIXA=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_uZnic4zEHH4LF0eRHZsqBDTF21Vb_m5IIeosj96Yy4BevwUtuhY1ORd3BasqM3RH0xhKfgQ9jy0dTANfEyhgoxp4052MBSRKsunXvx06PfkLpV8-ATZDgUQM_5NRp2Sn1nQ8tRaxDAwkzRlU4y_9rGjsBnUz2WFKYOl3L4Np-31H_YmutuSATJD57vM4-RSgfnvsPuuEqbZRkUVhvcjTJUOeshArja9hiL0CHBup3an5afzuAyhyBraG32WzwKTZFb7DezW15efiUMkOrdZyGPoKDhad8x4RjTKLbvq1-tVI8wYhquXzIP2wPeEqG64aEYa3bDSviwgP8azAJIq08cS6owXWxzf4wX4JCzqlw=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_tThksZhquhJp8oLJjjdM0y8GzB_kFwuNctOpbmS7EydXpguLrCMbv1sHCc9g7AbuZiOInyTHnicl78dFNUWD7HNTXKNyeh9cvng0cSmYi8tNniivZtTMphk0BujrL6qWnpR16tlJkjPok3eScmKt5TtyJdSoBk8aYb1-1eDuwp_HvXZ_HGlCVwCuodaYy1ESMA1pGBZRiRl6ked1EuHyBhhVMrT7uw_ApxK1oR_uD48omawCIE0VKAjR2Dq7ecaXrzSQ_Flcdzd7Q_=s0-d)
![\fn_jvn f'(x)=\frac{1}{3\sqrt[3]{x^{2}}}](https://lh3.googleusercontent.com/blogger_img_proxy/AEn0k_tmZSe2QfZCVpnPQGs5U8ehg7G09weVmcGyf3ndPTbOmVRFyjhIW87lDnrpRdFiOjDcizXrQUH_mVowesXaSVy9jWMNqJwjCNjhFS5OspaXLpGQgqO-EPNzKcSAGJgFjXkrTwDlcza3oO5L9ubM7Tp3ib2Hr6uW0At-bs1YOKTn6VIs0xZWncou6P6G=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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