Question

13 mark for review if ( f(x)=x^{5} ), then ( f^{prime}(x)= ) a ( x^{4} ) b ( 4 x^{4} ) c ( 5 x^{4} ) d ( 5 x^{5} )

Explanation:

Step1: Apply the power rule

The power rule states that if \(f(x)=x^n\), then \(f^{\prime}(x)=nx^{n - 1}\). Here \(n = 5\).

Step2: Calculate the derivative

Substitute \(n = 5\) into the power - rule formula. So \(f^{\prime}(x)=5x^{5-1}=5x^{4}\).

Answer:

C. \(5x^{4}\)