This English question involves literary analysis, grammar, or writing skills. The detailed response below provides a well-structured answer with supporting evidence and clear explanations.
ScanSolve AI Answer
To find the derivative of the expression 3x^3 + 2x + (3)/(2x), we will differentiate each term separately using the power rule and the sum rule. First, rewrite the last term to make differentiation easier. f(x) = 3x^3 + 2x + (3)/(2)x^-1 Step 1: Differentiate the first term, 3x^3. Using the power rule (d)/(dx)(ax^n) = anx^n-1: (d)/(dx)(3x^3) = 3 · 3x^3-1 = 9x^2 Step 2: Differentiate the second term, 2x. Using the power rule (d)/(dx)(ax^n) = anx^n-1 (where n=1): (d)/(dx)(2x) = 2 · 1x^1-1 = 2x^0 = 2 · 1 = 2 Step 3: Differentiate the third term, (3)/(2)x^-1. Using the power rule (d)/(dx)(ax^n) = anx^n-1: (d)/(dx)((3)/(2)x^-1) = (3)/(2) · (-1)x^-1-1 = -(3)/(2)x^-2 This can also be written as -(3)/(2x^2). Step 4: Combine the derivatives of all terms. The derivative of the entire expression is the sum of the derivatives of its individual terms: f'(x) = 9x^2 + 2 - (3)/(2x^2) The derivation of the expression is: 9x^2 + 2 - (3)/(2x^2) Send me the next one 📸