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The derivative of F(x) = (1/logt)dt for t ∈ [x^2, x^3], (x > 0) is (A) 1/3logx - 1/2logx

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The derivative of F(x) = ∫(1/logt)dt for t ∈ [x2, x3], (x > 0) is

(A) 1/3logx - 1/2logx

(B) 1/3logx

(C) 3x2/3logx

(D) (logx)-1. x(x - 1)

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Answer is (D) (logx)-1.x(x - 1)

We know that

 a and b are functions of x.

Therefore,

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