first you have to find the derivative of the equation f(x)= x 3/2 . To do this, you can use the power rule ( f ( x ) = x n goes to f ′ ( x ) = n x n − 1 ). so the derivative would be f'(x)= 2 3 x 2 3 − 1 , which can be written as f'(x)= 2 3 x . then you plug in 4 for x, and get 2 3 4 = 3 , so f'(x)=3
The derivative of the function f(x) = x^3/2 at x = 4 is 3 based on the power rule of differentiation. ;
To find f ′ ( 4 ) for the function f ( x ) = 2 x 3 , we first differentiate it to get f ′ ( x ) = 2 3 x 2 . After substituting x = 4 , we find that f ′ ( 4 ) = 24 .
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