This biology question covers important biological concepts and processes. The step-by-step explanation below helps you understand the underlying mechanisms and reasoning.
ScanSolve AI Answer
To differentiate "root x exponent of 2", we first write the expression mathematically and then simplify it before applying the differentiation rules. Step 1: Write the expression mathematically and simplify. "Root x" is written as sqrt(x). "Exponent of 2" means raising the expression to the power of 2. So, the function is f(x) = (sqrt(x))^2. For sqrt(x) to be defined, x must be greater than or equal to 0 (x 0). When we square a square root, they cancel each other out: f(x) = (sqrt(x))^2 = x for x 0 Step 2: Differentiate the simplified function. Now we need to find the derivative of f(x) = x with respect to x. Using the power rule for differentiation, which states that (d)/(dx)(x^n) = nx^n-1: (d)/(dx)(x) = (d)/(dx)(x^1) = 1 · x^1-1 = 1 · x^0 = 1 · 1 = 1 This derivative is valid for x > 0. The derivative of "root x exponent of 2" is: 1 3 done, 2 left today. You're making progress.