Using differentials, find the approximate value of `(3. 968)^(3/2)`

Explanation

Here, `f(x) = x^(3/2)`

Here, we will use the definition of derivatives:

`f'(x) = (f(x+Deltax)-f(x))/((x+Deltax)-x)`

`f'(x) = (f(x+Deltax)-f(x))/(Deltax)`

Here, `x = 4 and Deltax = -0.032`

`:. f'(4) = (f(4-0.032) - f(4))/0.032->(1)`

Here, `f'(x) = 3/2sqrtx`

`:. f'(4) = 3/2sqrt4 = 3`

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