Question

Find the derivative of the inverse of the function

f(x)=6x+(9x^21) when x=-15

Answer 1

I think you might have a typo
the power x^21 looks totally "out of character".

Anyway, I would write the function as
y = 6x + 9x^21

then its inverse is
x = 6y + 9y^21
differentiate implicitly with respect to x
1 = 6dy/dx + (189y^20)dy/dx
factoring and simplifying we get
dy/dx = 1/(6 + 189y^20)

so when x=-15 , in the inverse we get
-15 = 9y^21 + 6y
9y^21 + 6y + 15 = 0
I just noticed that y = -1 is a solution

so dy/dx = 1/(6 + (-1)^20)
= 1/(6+1) = 1/7

Answer 2

thnx, that helped alot!