Find the derivative of the following function.𝑓(𝑥)=𝑥6cos(𝑥)

To find the derivative of the function f(x) = x^6cos(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 that are being multiplied together. In this case, the two functions are x^6 and cos(x).

Step 2: Find the derivative of each function. The derivative of x^6 is 6x^5. The derivative of cos(x) is -sin(x).

Step 3: Apply the product rule. The derivative of f(x) = x^6cos(x) is (x^6)(-sin(x)) + (cos(x))(6x^5).

Step 4: Simplify the expression. The derivative of f(x) = x^6cos(x) is -x^6sin(x) + 6x^5cos(x).