If f(x) = x 2x 4x 8x 16x , then f' ( 4 ) is equal to

Step-by-step solution

Using the standard trigonometric identity x 2x 4x 2^ n-1 x = 2^n x 2^n x , we can simplify the given function for n=5 : f(x) = 32x 32 x Differentiating f(x) with respect to x using the quotient rule: f'(x) = 32 32x 32 x - 32x 32 x (32 x)^2 f'(x) = 32 32x x - 32x x 32 ^2 x Substituting x = 4 : 32x = 32 ( 4 ) = 8 We know that 8 = 0 , 8 = 1 , and ( 4 ) = 1 2 . f' ( 4 ) = 32(1) ( 1 2 ) - 0 32 ( 1 2 )^2 f' ( 4 ) = 32 2 32 2 = 2 2 = 2 Answer: 2