Question

5 multiple choice 1 point
what is the derivative of ( 5 x ^ { 8 } )?
( 35 x ^ { 7 } )
( 5 x ^ { 7 } )
( \frac { 5 } { 9 } x ^ { 9 } )
( 40 x ^ { 7 } )
( 5 x ^ { 9 } )
clear my selection

Explanation:

Step1: Apply the power rule

The power rule states that if \(y = ax^n\), then \(y^\prime=a\times n\times x^{n - 1}\). For \(y = 5x^8\), \(a = 5\) and \(n=8\).

Step2: Calculate the derivative

Substitute \(a = 5\) and \(n = 8\) into the power - rule formula: \(y^\prime=5\times8\times x^{8 - 1}\).
\(y^\prime = 40x^7\)

Answer:

\(40x^7\) (the fourth option)