Derivative of an inverse for Calc 1

[aero13]

Homework Statement

Find (f−1)'(a).
f(x) = 5x^3 + 3x^2 + 5^x + 4, a = 4

Homework Equations

I'm not entirely sure but I assume I have to use d/dx(f-1) = 1/f '(f-1(x))

The Attempt at a Solution

So far I switched y and x. Found dx/dy to be 15y^2 + 6y + 5. Then I switched dx/dy to dy/dx so the answer became 1/15^2 + 6y +5 and I plugged in 4 to get 1/269. But the answer is wrong

 

[dirk_mec1]

No, do not plug in 4 solve the equation being equal to 4.

 

[aero13]

Ok so I set 1/15y^2 + 6y + 5 equal to 4. Ended up with 1 = 4(15y^2 + 6y + 5) so 1 = 60y^2 + 24y +20. Do I factor it from here?