This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Sawa Shari, hebu tuendelee na tatizo (o). Ili kutatua tatizo (o), tutatumia kanuni ya mnyororo na kanuni ya nguvu. Tatizo ni: y = (1)/((3x-4)^2) Step 1: Andika upya usemi kwa kutumia kiashiria cha nguvu hasi. y = (3x-4)^-2 Step 2: Tumia kanuni ya mnyororo. Acha u = 3x-4. Kisha y = u^-2. Tafuta (du)/(dx): (du)/(dx) = (d)/(dx)(3x-4) = 3 Tafuta (dy)/(du): (dy)/(du) = (d)/(du)(u^-2) = -2u^-2-1 = -2u^-3 Step 3: Tumia kanuni ya mnyororo (dy)/(dx) = (dy)/(du) · (du)/(dx). Badilisha u na (du)/(dx): (dy)/(dx) = (-2u^-3)(3) (dy)/(dx) = -6u^-3 Step 4: Badilisha u na usemi wake wa asili (3x-4). (dy)/(dx) = -6(3x-4)^-3 Step 5: Andika jibu kwa kutumia kiashiria cha nguvu chanya. (dy)/(dx) = -(6)/((3x-4)^3) Jibu la mwisho ni: (dy)/(dx) = -(6)/((3x-4)^3) 3 done, 2 left today. You're making progress.