Did I do this problem right?
Find the first and second derative-simplify your answer.
y=xtanx
y'= (x)(sec^2 x)+(tanx)(1)
y'= xsec^2 x + tanx
y"= (x)(2secx)(secxtanx)+sec^2 x + sec^2 x
y"=2xsec^2 x tanx + 2 sec^2 x
= 2 sec^2x(x tan x + 1)
To determine if you did the problem correctly, we can simplify the answer to compare it with the correct solution.
Starting with the first derivative:
y' = xsec^2(x) + tan(x)
This expression seems correct.
Moving on to the second derivative:
y" = 2xsec^2(x)tan(x) + 2sec^2(x)
Again, this expression appears to be correct.
To verify, you can compare your answer with a known solution or use a graphing calculator or software to graph the original function and its derivatives. By examining the graph, you can check if your answer aligns with the expected behavior.
Remember, it's always a good idea to double-check your calculations and simplify your final answer to ensure accuracy.