161k views
4 votes
Find the derivative of p(x)=x ⁵⋅x.

A) p ′ (x)=5x ⁴
B) p ′ (x)=6x ⁴
C) p ′ (x)=6x ⁵
D) p ′ (x)=x ⁶

1 Answer

3 votes

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.

User Erikfas
by
7.5k points
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.