the derivative of ( f(x) = 6x^{3} ) is ( f(x) = bx^{k} ). find the value of ( b ). give an exact answer as…
the derivative of ( f(x) = 6x^{3} ) is ( f(x) = bx^{k} ). find the value of ( b ). give an exact answer as an integer.
Answer
Explanation:
Step1: Apply the power rule
The power rule states that if (f(x)=ax^{n}), then (f^{\prime}(x)=nax^{n - 1}). For (f(x)=6x^{3}), (a = 6) and (n=3).
Step2: Calculate the derivative
Using the power rule (f^{\prime}(x)=3\times6x^{3 - 1}). Simplify the coefficient: (3\times6 = 18).
Answer:
(18)