- #1
ishant
- 3
- 0
Homework Statement
^
Homework Equations
The Attempt at a Solution
y = tanx^cosx
lny = cosx(ln(tanx))
1/y(dy/dx) = (sec^2x * cosx)/tanx + ln(tanx)(-sinx)
at pi/4
1/y(dy/dx) = (1 * 1/sqrt(2))/1 + ln(1)(-sin(pi/4))
1/y(dy/dx) = 1/sqrt(2) + 0 ******* ln1 = 0
***
y = tanx^cosx => 1^(1/sqrt(2)) = 1 => 1/y = 1
***
dy/dx at pi/4 = 1/sqrt(2)
The answer is sqrt(2) NOT 1/sqrt(2)
What am I doing wrong?