Do not ever send me answers/solutions in french again. If not I will never use this scan solve again

Okay, I understand. All future responses will be in English. Here's the solution to your question: Step 1: Simplify the given function using logarithm properties. The function is y = (x^2 sqrt(x^2+1)). Using the logarithm property (ab) = a + b: y = (x^2) + (sqrt(x^2+1)) Rewrite the square root as a power: sqrt(x^2+1) = (x^2+1)^1/2. y = (x^2) + ((x^2+1)^1/2) Using the logarithm property (a^b) = b a: y = 2 x + (1)/(2) (x^2+1) Step 2: Differentiate each term with respect to x. Recall the differentiation rule for natural logarithms: (d)/(dx)( u) = (1)/(u) (du)/(dx). Differentiate the first term, 2 x: (d)/(dx)(2 x) = 2 · (1)/(x) = (2)/(x) Differentiate the second term, (1)/(2) (x^2+1). Here, u = x^2+1, so (du)/(dx) = 2x. (d)/(dx)((1)/(2) (x^2+1)) = (1)/(2) · (1)/(x^2+1) · (2x) = (2x)/(2(x^2+1)) = (x)/(x^2+1) Step 3: Combine the differentiated terms. (dy)/(dx) = (2)/(x) + (x)/(x^2+1) Step 4: Combine the fractions into a single expression. Find a common denominator, which is x(x^2+1). (dy)/(dx) = (2(x^2+1))/(x(x^2+1)) + (x · x)/(x(x^2+1)) (dy)/(dx) = (2x^2+2 + x^2)/(x(x^2+1)) (dy)/(dx) = (3x^2+2)/(x(x^2+1)) The final answer is (3x^2+2)/(x(x^2+1)). Last free one today — make it count tomorrow, or type /upgrade for unlimited.