Question

Find the derivative of the function

y = 4x^4 - 15x - (5/x^3)

y' = 16x^3 - 15 and I'm confused on how to deal with (5/ x^3).

Answer 1

5x^-3

Answer 2

would that be clearer to deal with?

Answer 3

apply division theorem used in diff

Answer 4

5/(x^3) =5*x^(-3)

Answer 5

or do as @mathsmind said

Answer 6

recall nx^n-1

Answer 7

y'=16x3-15-5(-3)/x4
=16x3-15+15/x4

Answer 8

ah okay. so I I had something like 5 / 2x^3 it would be equal to 10x ^-3 then the derivative of that -30x ^-4?

Answer 9

\[\frac{ 5 }{ 2 }x^{-3}\]

Answer 10

try it again now...

Answer 11

\[\frac{5}{2} (-3) x^{(-3-1)}\]

Answer 12

-15/2(x)^-4

Answer 13

can you visualize the pattern now?

Answer 14

let 5/x^3
=5x^-3
=-3(5)x^-3-1
=-15x^-4

Answer 15

I get that part I just didn't know how to deal with that fraction (5/x^3). Thanks for clarifying this.

Answer 16

nx^(n-1), for n = -3