Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function. y=  int((3t+(t)^(1/2))^(1/2)))dt, t=7...tanx)) Use Part 1 of the Fundamental Theorem of Calculus to find...

Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function.

y=  int((3t+(t)^(1/2))^(1/2)))dt, t=7...tanx))

Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function.

y=  int((3t+(t)^(1/2))^(1/2)))dt, t=7...tanx))

y' = ________________

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`y=int_7^(tan(x))sqrt(3t+sqrt(t)))dt`

The first part of the theorem says,if,

`F(x) = int_a^xf(t)dt` then,

`F'(x) = f(x)`

In our case, we have tan x instead of x, so we can't apply this theorem straight away, so we need a substitution. we will use

`u =tan(x) `

so ,...

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