Calculus

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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?

  • Calculus -

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

  • Calculus -

    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)

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