Hello, I am getting confused as to how to differentiate this function:

tant + tsec^2t

I attempted it incorrectly as such:

sec^2t + (1)(sec^2t) + (t)(2sint/cos^3t)

by using product rule for the second part of the sum and using 2sinx/cos^3x as the differentiation of sec^2t

Can someone please show me where I went wrong ?

Thanks kindly