What is the derivative of (x + 1) sin x?

To find the derivative of the function (x + 1) sin x, we will use the product rule. The product rule states that the derivative of two functions multiplied together is the first function times the derivative of the second function plus the second function times the derivative of the first function.

Step 1: Identify the two functions in the product. Here, the first function is (x + 1) and the second function is sin x.

Step 2: Find the derivative of the first function, (x + 1). The derivative of x is 1 and the derivative of 1 is 0, so the derivative of (x + 1) is 1.

Step 3: Find the derivative of the second function, sin x. The derivative of sin x is cos x.

Step 4: Apply the product rule. The derivative of (x + 1) sin x is (x + 1) * (cos x) + sin x * 1.

Step 5: Simplify the expression. The derivative of (x + 1) sin x is (x + 1) cos x + sin x.