Turunan 3
Contoh 4 :
Turunan pertama dari
![\fn_jvn f(x)=\sqrt[3]{x}](https://lh3.googleusercontent.com/blogger_img_proxy/AEn0k_vo_7Mev0zQqJdxaviMexOE27G2OJJrTDjIsm4zz4Qj9AxL2oNYMrXmh5H0sdDGPc747efeNO3lpBneznkWaUIuPyk09CjSSceVRcnrhWdPRZFsA9UB2ppIKdQ_DE8xWE6MviCHTvhYCneciQ=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_vevZuK8AsBEkyr2hTka2TCM6LuPaFn3V-y2k-ExZtkgbpuUFO_TtenRTij7K9KGC3Gbi5BcR8kCWLXC7tbFj2oFC_VtV3oBAIJQgWbHGfYIm3Sg2HqStiqHV6K1JEwUojHpEFqqtM52gLwd4owlAN5fHHPPkZsrvtrnl23jIHN6-rOCDYLS9ikx42_xksYSg96qM0nrOlyNa3PUieer3SXRfI3lPepkqiuKwHRtsOwU4eCTCcGbYfwDE_ZlRE_FuO24sZBuRC2zj8ExyjXMhfMr6J7YBFx=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_vp1dhprAXLI-aLRwcOqFlvIFjX58hrv8lzF2tBQrC6QKKjEeM0VOPlC5Ur2bUd1f_Gdyo4hdH-GnyzV-8Q7kor81EIsID6HZ2FmIb2zmPtzeWWNmmFbdc0daPcn1Xpt8vpAmMgJYIekUe9tx5WcSmwfPjujUAkiIZ_tLjyulc79kNK4MF2O5ieIWpCmKiBQfBG5o1__6mYyYHs61gc74k8-X-aPyFBQCayFH5W9M7QWDN97VIzQh-o4nFmZ1RNG6k4zr2VCS0vK_BwY-ARrZrCGzxs3JeZ2S3bgQJ0IFBhs2-UfHXHqENlFeCtw6uF9c0_fV5I1AfXt5cZe-8WyUOvLJSVa2ZtBnxSbdstgVApw9gIIo44o0bn-PH1oL0feQrOOvol5CC8kDD9CBdiChsgVDMM4SEWF4lfWt0BUc41BoNb1Sx7zMFZHDD0gxYre32_M-_sWp8kDHZocY5sy32wB9IlISXFuPbIUz4Rx5DdI4G9fOIOIRtjPFS7R9fTYhEoTCrDHbRYcyt70gfiEzyMZbxYImqVKFlkq2TkZi8Cf23U8UY95N6zn6j_ybz-P8lg08y9y75QpeJfWOvcj1sfvyc1lsYu9zIVwPYzL0Tz=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_sZrmoHbJxxZOpMQXRI1hPM1tO9bCiqVYbvF2ONTxKFu6C56raX3660bs9FISGehakvUK4EYmtdXv5quHu31VgZHKGM_t-YyomuGTvIVm092rJtXYU56ldpr3ZuXj5PyhuyTRTfTk9tlcRuuijuromUPmaNfrkw-hs9ppADQSuyjtf3M_hZqF3iKo6cXQ__h4hb-K-tqHU5dOhdCsrt1qiwqp8B4VWNQGxfY8Qthja1TrbAtFvBjkXkXjtFL9yQcDXPAOXzR3HpV6oL_gEtLpUJnQgnPq7IKiQ202Qt78zeeTru3_Ih1lNTDWyteKjaOshqIGq0cFzSotJcnhkuPxr8SY81sI3vSKJg6B9h5d_DiGVI6UVoKcOLh3OYbU4w2Smi-pYcUA92Gw=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_ut656zIktHWlODdKx3pQrzD3Zv56lCtDY9g3R-RNV1I6PDh6SDNKbwqo-uAfj_UUsZnVnU4laZihn4k8xqS00ygSppW5WN_v2xfq9A9R801c34OjH1uJ99felbB_1TipX-6uZHVddP6dJOfNnAQGGVVM7DG6wjd-CI3v4NDVK9KKcpzG4YK5cAYTbngHqZ6NZf_DnNdiA8Pb1Dr8BLPI4dodx0iciSuDsyYUuFPIhVE7gsQtkQDbmTTUf1515OWXuNv19ymMjFLYHbJMfKdFb-9AfB2imXDvCHEgfXKihRU8kxwpkaELWeznyhDPN6NTlRRHKFe7bfPijqBHU1zMfpu4QDKezWskT7wNAAS9N_E0436tKwakMEr-PoVT0xoaL7Q3IohA=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_ty-wfq6TWP9DcawKysRSxSEFvWYi5uRud8ZeSoXyalIQPqDIdMFAWQtgzFdN2hvAaguPuTpVkKtle6utz1Xt1BmExlJQR7z1TF6kFh1L1fhXNuXfhl4_-tq6FInh4oK5D7ecyPggUNYic7KjMoNrG5-y4rAz58EcuNKs9jsKmmxDHklyhe9oPF6bjUPO7UNu8LtW084NKysfKVXDhlVowp386gR50PrZ7c-EPScCFPi7oOv27RPDqaYN_w3IYE4r6LKuPsUtOUEAUARCnaQefPuBxs0RqDBdbhvWMolyQ3-zMjViLRo-ZtBUm4g_10OOj4NlXfytBissBRtGJ45z-FgDmq-gPr-S1e5Gkc1zg=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_vGE5--jc_SEQKKrh_vGWtkeAyJt2qUYlwD5Z2Kv-rmvNtPLXBhaq4xvWGOkKOE5iaiJ_oqfHflJoJDTfzTazJnDHAQWxpeDZH8ZKPS1EFJBh5dIk2YfzcqJhAaN7kJxLZOloIJkKbekc-FBJwED452Qi5n_aTXDUFY_HyE6zLtz-1q1ZMoIM2MGIcOCmojay-Wam728GUMVEv83d-Ldb1C5i2-J-5dfQKLdd-4cg3tpXjneDJFa0MpqXKqlW6fIGzUYtxAtllgyauo=s0-d)
![\fn_jvn f'(x)=\frac{1}{3\sqrt[3]{x^{2}}}](https://lh3.googleusercontent.com/blogger_img_proxy/AEn0k_vrE6D6c-D99WvR9eyTAlRRWWbBqw4m0gLiwWEAmnjBcAqYvsygu9hhOzkFZCBEU4LLH4g3ue_9FQIi9VndGZw44rIcio79FvM6R6_Ja9oZUe-Ywjjg7s2LSrL-M5KpOjbUY0VbQ_AgkWk22Tg2fqTlNPITcTNKGdYyxEgWU3tQcIQw4dyI2BYJhN51=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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