Question

the derivative of ( f(x) = 6x^{3} ) is ( f(x) = bx^{k} ). find the value of ( b ). give an exact answer as an integer.

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:

\(18\)