If y = ⁻¹ ( 1 - 4^x 1 + 4^x ) , then dy dx at x = 1 is

Step-by-step solution

Given y = ⁻¹ ( 1 - 4^x 1 + 4^x ) Let 2^x = . Then 4^x = (2^x)^2 = ^2 . Substituting this in the given expression: y = ⁻¹ ( 1 - ^2 1 + ^2 ) y = ⁻¹( 2 ) Since 2^x > 0 , > 0 (0, 2 ) 2 (0, ) . Thus, y = 2 = 2 ⁻¹(2^x) . Differentiating with respect to x : dy dx = 2 1 1 + (2^x)^2 d dx (2^x) dy dx = 2 1 + 4^x 2^x 2 At x = 1 : dy dx = 2 1 + 4^1 2^1 2 = 4 2 5 Answer: 4 2 5