If f(x)= cosec ⁻¹ [ 10 6 (2^x )-8 (2^x ) ] , then f^ (x)

Step-by-step solution

aligned & f(x)= cosec ⁻¹ [ 10 6 (2^x )-8 (2^x ) ]= ⁻¹ [ 6 (2^x )-8 (2^x ) 10 ] & Here (6)^2+(-8)^2=(10)^2 & Let = 6 10 and = 8 10 & f(x)= ⁻¹ [ (2^x ) - (2^x ) ]= ⁻¹ [ (2^x- ) ] & f(x)=2^x- f^ (x)=2^x 2 aligned