5 multiple choice 1 point\nwhat is the derivative of ( 5 x ^ { 8 } )?\n( 35 x ^ { 7 } )\n( 5 x ^ { 7 } )\n(…

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

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

Answer

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)