Express as,Originally Posted by c_323_h
Let,
, thus
Thus,
Thus,
Substitute back,
Hello, c_323_h!
Find the derivative:
Differentiate implicitly: .
Then we have: .
Rearrange terms: .
Factor: .
Therefore: .
2^u + 2^{-u})^{10}" alt="2)\;f(u)\:=\2^u + 2^{-u})^{10}" />
Take logs: .
Differentiate implicitly: .
We have: .
Since , we have: .
Use the substitution rule:
We have: .
Let:
Substitute: .
You can finish it now . . .
We have: .
Let:
Substitute: . . . . got it?
Hello again, c_323_h!
Differentiate:
. . . . . **
Evaluate the integral: .
In the denominator, complete the square:
The integral becomes: .
. . Let
. . Note that: .
. . . . . . . . . .
Substitute: .
Back-substitute
We have: .
So we have: .
. . .
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In #2, we have: .
Let: . . . and:
Then . . . and
Since , is in this right triangle:Code:* /β| / |1 /α | * - - - * t
Since is the other acute angle.
That is: .
Hence, the function is: .
No wonder the derivative is 0 . . .