SOLUTION: Can someone please show how to take the implicit differentiation of this problem? Compute (d^2y) / (dx^2) of: y^2sec(x) = 1 Please explain Thank you

Algebra ->  Equations -> SOLUTION: Can someone please show how to take the implicit differentiation of this problem? Compute (d^2y) / (dx^2) of: y^2sec(x) = 1 Please explain Thank you      Log On


   

Question 1025928: Can someone please show how to take the implicit differentiation of this problem?

Compute (d^2y) / (dx^2) of: y^2sec(x) = 1
Please explain
Thank you
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Use the chain rule,
y%5E2%28tan%28x%29sec%28x%29dx%29%2Bsec%28x%29%282ydy%29=0
Factor out sec(x).
y%5E2tan%28x%29dx=-2ydy
dy%2Fdx=-%28ytan%28x%29%29%2F2
Now differentiate again using the chain rule,
%28d2y%29%2F%28dx2%29=-%281%2F2%29%28y%2Asec%5E2%28x%29%2Btan%28x%29%28dy%2Fdx%29%29
Substitute,

%28d2y%29%2F%28dx2%29=-%28y%2F4%29%282sec%5E2%28x%29-tan%5E2%28x%29%29%29