This chemistry question involves key chemical concepts and calculations. The detailed solution below walks through each step, from identifying the reaction type to computing the final answer.
ScanSolve AI Answer
My apologies for the previous misunderstanding. I will now solve the problems labeled c and d directly from the image you provided. c) Differentiate y = _b (3x-2). Step 1: Recall the differentiation rule for a logarithm with an arbitrary base. If y = _b(f(x)), then (dy)/(dx) = (1)/(f(x) b) · f'(x). Step 2: Identify f(x) and find its derivative. Here, f(x) = 3x-2. The derivative of f(x) is f'(x) = (d)/(dx)(3x-2) = 3. Step 3: Substitute f(x) and f'(x) into the differentiation rule. (dy)/(dx) = (1)/((3x-2) b) · 3 (dy)/(dx) = (3)/((3x-2) b) The derivative of y = _b (3x-2) is (3)/((3x-2) b). d) Differentiate y = _e ( x). Step 1: Rewrite the function using the natural logarithm. Since _e x = x, the function can be written as y = ( x). Step 2: Recall the differentiation rule for the natural logarithm. If y = (f(x)), then (dy)/(dx) = (1)/(f(x)) · f'(x). Step 3: Identify f(x) and find its derivative. Here, f(x) = x. The derivative of f(x) is f'(x) = (d)/(dx)( x) = ^2 x. Step 4: Substitute f(x) and f'(x) into the differentiation rule. (dy)/(dx) = (1)/( x) · ^2 x Step 5: Simplify the expression using trigonometric identities. Recall that x = ( x)/( x) and x = (1)/( x). (dy)/(dx) = (1)/( x) x · (1)/(^2 x) (dy)/(dx) = ( x)/( x) · (1)/(^2 x) (dy)/(dx) = (1)/( x x) This can also be written as x x. The derivative of y = _e ( x) is (1)/( x x). 3 done, 2 left today. You're making progress.