Question

Find f'(x)
f(x)=(1-2x^2)^3

Answer 1

Answer: f'(x) = 12x + 48x³ - 48x⁵

Explanation:

f(x) = (1 - 2x²)³

= (1 - 2x²)(1 - 4x² + 4x⁴)

1 - 4x² + 4x⁴

-2x² + 8x⁴ - 8x⁶

= 1 - 6x² + 12x⁴ - 8x⁶

f'(x) = 0 -2(6)x²⁻¹ + 4(12)x⁴⁻¹ - 6(8)x⁶⁻¹

= 12x + 48x³ - 48x⁵