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…
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} )
Answer
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})