Question

If f(x) = integral of 1/ (sqrt of t^3 +2)dt, then f'1 = ?

Answer 1

Differentiating an integral removes the integral.

f(x) = integral of dt/sqrt(t^3 + 2)
f'(x) = 1/sqrt(x^3 + 2)
f'(1) = 1/sqrt(1^3 + 2)
f'(1) = 1/sqrt(3) = sqrt(3)/3.


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