Final answer:
To find the derivative of the function p(x) = x⁵ ⋅ x, we simplify it to x⁶ and then apply the power rule to obtain the derivative, which is p'(x) = 6x⁵. The correct option for the derivative is B) p'(x) = 6x⁴.
Step-by-step explanation:
The student has asked a question regarding the derivative of a function in mathematics. To find the derivative of p(x) where p(x) = x⁵ ⋅ x, we first simplify the function.
Observing that the function can be rewritten as x⁵ ⋅ x = x⁶ since multiplying two expressions with the same base, you add the exponents. Now, we can apply the power rule to find the derivative:
p'(x) = d/dx (x⁶) = 6x⁵
The correct answer is therefore B) p'(x) = 6x⁴, which is obtained by subtracting 1 from the exponent and multiplying by the original exponent per the power rule.