Turunan 3
Contoh 4 :
Turunan pertama dari
![\fn_jvn f(x)=\sqrt[3]{x}](https://lh3.googleusercontent.com/blogger_img_proxy/AEn0k_tWvj5vQ3NSmAl_cHuB8FByW-B8SlTMd4Nlec1PeNMzMQxkjIxcgAJAA6CrOnlvh1Oht7PQ-ZSqw4M32SHOqaXrkSTH_jdaDnN_5n5XmQ0gZUHwoiUy_ignTHvHKNy7Z086dcrrxHeM61YbtQ=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_t7HuRtN1v_9qxezz70whLxAsGxSYTUH47OcEY4EH7OJQwQcSFpcXOvu5GGnKGwyWRum2FirDjAIpAAKAKnBtYCrKC9KQGXh5mSXST1SaWhU6ED_5nDeYC9nRdM94NG5FoUPrtK8BGKGxqz0zte455dR-qi3iiQdFmugCybQCWfUd-XZ4GpO5YL5MtwPDnm_Vywh74_5v8anp8VzFMmAw3cpzn1vR3wI22ecDx1o3IFbD7xi6aga38-O3cDIDQAz7LRwYTK3vcoomMQEm696RZ8Vrx2Vr9I=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_spS-w0BiT77gmOAOc-CDpTaOXfwMDIXgGYch0HUbhRW7jOECXmQ-NQJq-k8n4XGUQ7snZdHhaOg9_YYomwEW1bn4Sf5l5w2dUPTnpFDDkFT2Y6-gnYzQgY8qcCKzp6BpS9x6kipEqEmhUJBEDV3kUDlZ00DL6sfeovwcAw10QlQZ7rHvFN68OeHDU5mwDhzTVhcKbnwUTMg6qaCDjDGb39s3-zfWs6s4Xz3TWx5DrZJ7TFfPXFah_7FWYY_Ki3jol9qLuHtKMSZg71cIOEAB6I0drYn0mowAWCK3HY4Sm7hxZHXQClDzvIf_2YkSsldg0W62jXW1o9cA3Rhr0owPn5USCYLUrdxpIMGfHL5lul62Jofee-oU3SDFVG8AW-02NDf4p_XGH60WW9fMZFbb1VF1hI1wMawaOrDkq9G9wcg_0CDYD-MrOPLy4QpqPL28wI5ZEa7RmIwDI_B7mSEC9aaQ3HPxLP7bVjx4rn-Exa8eZ75OqeFiaQMFPy_W5OhxDIr5nIYLrnXACrflVxTNzoMfhDQ-wIvzXF83-NCuOjl1VfErxCCfLY3PFIfIeLHy_VGn0GICGR5wVwMt-69eCr8tAv8fky0MsSZM1fjG8K=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_syydL9NVU6FpRDjL4Ykv8B14Xv9Ksknd4NV2mJAItNrVMxXAzIvU8pOnKUU3o6TwXsP9OJ0rQkE9aymHRs_Df0_DWVXI3pUpuF1ZxGeXdEpRlDwQ1zKhI1N0zL1g2Rk7VWOjWp47rYmw9rdmYyA8jf2qbF-28ccAgfwjrOrQ49_FkrNAy_AJnpPKYZda_AA5D_h52luhxBDsExtWPGCB3aAcUN1JsfmSMNO0vOj-Z-y3mkzHnJ2HhQ_ex2PjHJVSiRMTfO1-ro1Ybs-gUsxUEwcheSxh6lTzIcBjxnGq3Smh2-kr1vriVH6sfByWOCsrCXpy_dYOduDCdBXzTZoHzBAk9nfZn64NbOoMkg6dRjipF8aczmoDAHQjvZ10KW0_dpgFi3XhOSeg=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_u0TpczAt4G-HL9B7DpcB9odx-sN2kp_BiT0uSvbCcYpVupzBqL6yXqXN0a1lvp3WLlWd3QClhgqxWzxgJFY6RzId8Gk6JhCNxLfOPkAYeYbvdwnSe1xBW-xw--RzyOkg-bVN-oEML2ifLWMK62qrNjiwKZ7H8mlcZbdPl8uOpbMW5yheZeXc01R8-tuiMC24Tp4kuHLT-7CMZZKFoyUxD7kVeCyVq3oD8uyAL6blqaaJinmYlgXCyys3MUppP2HLiylIxjv2GaJeV6BqqmA8BY11Asw1nx3yhRVBx6Lnw9_ic1oUTm1xdnbef9LXOQYF9JlxXdoq5GPem4m8VH2ec-CmAKWY0wWC528ULAgx400u5F4_bTUubJLS5suMrHfMFDotls1Q=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_ujugkJyyFHXFyN8K1Sbft7IV8ifpxRlN0EQb_goa5Ei2UaYEK4ZdkmNeZMeMI4wsKrXz3N6UM4fUWHtsX8lYPDWeorZTGK82YsFzTGjynZcxfBaCoadTI7iYQ966ILrnZVatFBEunFLJHFgkTrhlAFlRmC1OmlLWYCXLQukyis0zeloLe68MlaAg0dDKYaLk-hDj5VxFENY5_Y4oJZoOKAsDmt4SG-CmtH5vRR6-khuHJ8M_QhuWI4wZVHQR-JIVczF1M_rxHAJ5fqbddOETFiPr2EG5WGKhMtQsr2BDz6bCTYPOV3uTTToWrqbJiqdbTAjUsv3sZ3xuSXTYePr_mbaEkE_y_MmBNX2YebQ4U=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_tou-XIDHe42-HAuIqI4DbsE7yTaemWMcIKoA1Iipfy7zIq3_90iaKjwy7dfqdMoE8Vm6zqw6Ik8UBryXjfRHAtlSzkkTM8Xzshw9zEXRWgGPDb6cGYWhg1r-4l7q2mujZ2Y4ntEg70KyGqjLtLKzDH6YP58PHFFnLVltfUYmfWKicruoAqg5ld5vCj0CbseFB3tjJ4DRKDMsXi4rjerLIUNfhjEdlMt6sJv7sAotZCNArtz1lwDkhaLHWhOe8QsvBTn9a1fdr5L3J3=s0-d)
![\fn_jvn f'(x)=\frac{1}{3\sqrt[3]{x^{2}}}](https://lh3.googleusercontent.com/blogger_img_proxy/AEn0k_t8T3mHJmxJmARSaYMc8dmoqK6s38uQ2cjm7nxwAPWv2GV_JyqBbDkFxpZlUxv7pu3hqeOOsxyMG-HrHIX-6TcLSEoDOBDEUwRorwf8h5Y-pSf2bGiop-z0O7d1HK_z2MB4aSCx1IlsdZOZk5JiozhEegJwnm4b5g6hzqbStfZ4yZzHqO6ABFt9U36-=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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