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
2) Differentiate the following a) y = 3x^-3 Step 1: Apply the power rule for differentiation, which states that if y = ax^n, then (dy)/(dx) = nax^n-1. Here, a=3 and n=-3. (dy)/(dx) = (-3) · 3x^-3-1 Step 2: Simplify the expression. (dy)/(dx) = -9x^-4 The derivative is -9x^-4. b) y = (4)/(x^2) Step 1: Rewrite the function in the form ax^n. y = 4x^-2 Step 2: Apply the power rule for differentiation. Here, a=4 and n=-2. (dy)/(dx) = (-2) · 4x^-2-1 Step 3: Simplify the expression. (dy)/(dx) = -8x^-3 The derivative is -8x^-3. That's 2 down. 3 left today — send the next one.