The discussion centers on finding the derivative of the function y = tan(x)^cos(x) at x = π/4. The user initially calculated dy/dx as 1/sqrt(2) but later confirmed that the correct value is sqrt(2). The confusion arose from an incorrect evaluation of sec^2(π/4), which equals 2, rather than 1. This highlights the importance of accurately applying trigonometric identities in calculus.
PREREQUISITESStudents studying calculus, particularly those focusing on differentiation of trigonometric functions, and educators looking for examples of common mistakes in derivative calculations.
Hello ishant. Welcome to PF !ishant said: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
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y = tanx^cosx => 1^(1/sqrt(2)) = 1 => 1/y = 1
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dy/dx at pi/4 = 1/sqrt(2)
The answer is sqrt(2) NOT 1/sqrt(2)
What am I doing wrong?
SammyS said:Hello ishant. Welcome to PF !
What is sec2(π/4) ?