Answer: f '(4) = 16/101
Explanation:
37 +5f(x) + 2x² (f(x))³ = 0
Take derivative of both sides
0 + 5 * f '(x) + 4x (f ( x))³ + 2xx*3 * (f(x))^2 * f '(x) = 0
5 * f '(x) + 2xx*3 * (f(x))^2 * f '(x) =
- 4x (f ( x))³
[5 + 2xx*3 * (f(x))^2 ] * f '(x) =
- 4x (f ( x))³
[5 + 6xx * (f(x))^2 ] * f '(x) =
- 4x (f ( x))³
f '(x) =
- 4x (f ( x))³ / [5 + 6xx * (f(x))^2 ]
f '(4) = -4*4 f(4)^3 / [5 + 6*4*4*f(4)^2]
f '(4) = -16*-1 / [ 5 + 96 ]
f'(4) = 16/101
from MysticAlanCheng