How do you solve this derivative? and which answer do you think is the closest?

Question

............ x
If f(x) = ò t^6 dt, then f ''(x) =
.............2


a. x^5 /5
b. x^4
c. x7 /7
d. x^4 /4
e. 6x^5
f. x^2
g. x^2 /2
h. x^6 /6
i. x^7 /7
j. none of these

Answer 1

e. 6x^5

f'(x) =x^6
and so
f''(x)=6x^5 .

Answer 2

............ x
If f(x) = ∫t^6 dt = (1/7)[x^7 - 2^7]
.............2

=>
f'(x) = d((1/7)[x^7 - 2^7])/dx = x^6

=>
f''(x) = d(x^6)/dx = 6x^5

letter (e) is correct.

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