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
Here's the solution for the differentiation problem: (b). If y = 3x^5, find (dy)/(dx), (d^2y)/(dx^2) and (d^3y)/(dx^3) Step 1: Find the first derivative, (dy)/(dx). Apply the power rule for differentiation, (d)/(dx)(ax^n) = anx^n-1. y = 3x^5 (dy)/(dx) = 3 · 5x^5-1 (dy)/(dx) = 15x^4 Step 2: Find the second derivative, (d^2y)/(dx^2). Differentiate the first derivative, (dy)/(dx), with respect to x. (d^2y)/(dx^2) = (d)/(dx)(15x^4) (d^2y)/(dx^2) = 15 · 4x^4-1 (d^2y)/(dx^2) = 60x^3 Step 3: Find the third derivative, (d^3y)/(dx^3). Differentiate the second derivative, (d^2y)/(dx^2), with respect to x. (d^3y)/(dx^3) = (d)/(dx)(60x^3) (d^3y)/(dx^3) = 60 · 3x^3-1 (d^3y)/(dx^3) = 180x^2 5 done, 0 left today. You're making progress.