A calculus problem by Devashish Katoriya
Calculus
Level
2
If x=2cosA - cos2A
and y = 2sinA - sin2A ,
Find double derivative of y with respect to x at A = (pi) / 2
The answer is 0.5.
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1 solution
I'm just presenting my solution but I think I got some mistakes, so feel free to make your feedback
let f(A) = y = 2sinA - sin2A and
g(A) = 2cosA - cos2A
get the second derivative of f(A) which is :
=> 2sinA - sin2A
Then evaluate at A = pi/2 :
=> -2sin(pi/2) + 4sin2(pi/2)
= -2(1) + 4(0)
= -2
get the second derivative of g(a) which is
=> 2cosA - cos2A
Then evaluate at A = pi/2 :
= -2cos(pi/2) + 4cos2(pi/2)
= 0 + 4(-1)
= -4
Then get the derivative of y with respect to x which means
dy/dx which is -2 / -4 = 1/2 or 0.5
note that just like in parametric equations
dy/dx = second derivative of y over first derivative of x
which is what I'm thinking for sometime because if that is the case, then the answer should be 1
I'm not so sure about this but I hope someone could help me. I got the answer anyway, just bothered by the solution