Question

I need help with finding first and second derivative--simplify your answer.
Y=xtan(x)

I solved first derivative
xsec^2(x) + tan(x)

I don't understand how to get the first...can someone show me the steps with explanation?

Answer 1

Sorry I don't understand how to get the second derivative, I gsolved the first derivative already

Answer 2

well, the derivative of tan(x) is sec^2(x) that part is trivial.

derivative of x(sec^2(x)) is

y=uv
y'=vu' + uv'
let u=x v=sec^2=cos^-2
u'=1 v'=-2cos^-3*(-sin)
v'=2tan(x)sec^2x

so overall, the

f"=2x tan(x)sec^2(x)+sec^2(x)+sec^2(x)