SOLUTION: If y(x) = ln(secx + tanx), determine the third derivative of y(x), i.e., find d^3y/dx^3.

Algebra ->  Equations -> SOLUTION: If y(x) = ln(secx + tanx), determine the third derivative of y(x), i.e., find d^3y/dx^3.       Log On


   



Question 1200825: If y(x) = ln(secx + tanx), determine the third derivative of y(x), i.e., find d^3y/dx^3.
Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!
y%28x%29+=+ln%28sec%5E%22%22%28x%29%5E%22%22%5E%22%22+%2B+tan%5E%22%22%28x%29%29

Use the formulas: d%2F%28dx%29ln%28u%29%22%22=%22%22%28du%2Fdx%29%2Fu%5E%22%22, 
  d%2F%28dx%29sec%5E%22%22%28u%29%22%22=%22%22sec%5E%22%22%28u%29tan%5E%22%22%28u%29expr%28du%2Fdx%29,
and d%2F%28dx%29tan%5E%22%22%28u%29%22%22=%22%22sec%5E2%28u%29expr%28du%2Fdx%29

we have:

dy%2Fdx%22%22=%22%22

dy%2Fdx%22%22=%22%22

dy%2Fdx%22%22=%22%22


dy%2Fdx=sec%5E%22%22%28x%29

d%5E2y%2Fdx%5E2=sec%5E%22%22%28x%29tan%5E%22%22%28x%29



d%5E3y%2Fdx%5E3=sec%5E3%28x%29%2Btan%5E2%28x%29sec%5E%22%22%28x%29

d%5E3y%2Fdx%5E2=sec%5E%22%22%28x%29%28sec%5E2%28x%29%2Btan%5E2%28x%29%5E%22%22%29

Use formula 1%2Btan%5E2%28u%29=sec%5E2%28u%29 as tan%5E2%28u%29=sec%5E2%28u%29-1



d%5E3y%2Fdx%5E2=sec%5E%22%22%28x%29%28sec%5E2%28x%29%2Bsec%5E2%28x%29%5E%22%22-1%29

d%5E3y%2Fdx%5E2=sec%5E%22%22%28x%29%282sec%5E2%28x%29%5E%22%22-1%29

Edwin