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Find f"(x) for the function.

f(x)= x^2+√x

A. 2x^(3/2)+1/x^(3/2)

B. 8x^(3/2)-1/4x^(3/2)

C. 2x^(3/2)-1/x^(3/2)

D. 8x^(3/2)+1/4x^(3/2)

Is it B. Please help me explain this one. Thanks

It is none of the above. When differentiation a function (powers of x), its degree should go down by 1. So taking the second derivative will decrease the degree by two. Your function f, is made up of the sum of a function whose degree is two (first function) and a function who degree is half (second function).

After two derivative, the first function will have degree zero. That would be a constant function. Similarly, after two derivatives, the second function will have degree half minus two which is negative three halves (or -1.5). And none of the choices above is a constant plus a function of degree minus three halves.

The correct answer should be 2 - 1/(4x^1.5).

Calculus

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