If F(x)=∫(e,x)log t dt for all positive x,then F'(x)=?(a)x(b)1/x(c)log x(d)xlog x(e)xlog x-1

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IfF(x)=∫(e,x)logtdtforallpositivex,thenF''(x)=?(a)x(b)1/x(c)logx(d)xlogx(e)xlogx-1IfF(x)=∫(e,x)logtdt

If F(x)=∫(e,x)log t dt for all positive x,then F'(x)=?(a)x(b)1/x(c)log x(d)xlog x(e)xlog x-1
If F(x)=∫(e,x)log t dt for all positive x,then F'(x)=?
(a)x
(b)1/x
(c)log x
(d)xlog x
(e)xlog x-1

If F(x)=∫(e,x)log t dt for all positive x,then F'(x)=?(a)x(b)1/x(c)log x(d)xlog x(e)xlog x-1
With the help of this formula we can solve this quesion easily.
d/dx ∫(a→b) ƒ(t) dt = b'ƒ(b) - a'ƒ(a)
For F(x) = ∫(e→x) log(t) dt,
we have F'(x) = d(x)/dx · log(x) - d(e)/dx · log(e)
= 1 · log(x) - 0
= log(x)
Therefore the answer is C