Question

Find the derivative of the function s(x) = x⁵ * x

Answer 1

The derivative of the function s(x) = x⁵ * x is found by first simplifying the equation to s(x) = x⁶, then applying the power rule, resulting in the derivative s'(x) = 6*x⁵.

Step-by-step explanation:

The student seeks the derivative of the function s(x) = x⁵ * x. This is a calculus problem involving the application of basic differentiation rules. First, we simplify the function by combining the like terms, which gives us s(x) = x⁶. To find the derivative, we apply the power rule. The power rule states that the derivative of x^n, where n is a real number, is n*x^(n-1). In this case, the function s(x) = x⁶ can be differentiated as follows:

s'(x) = d(x⁶)/dx = 6*x⁵

So the derivative of s(x) when x⁵ is multiplied by x is 6*x⁵.