The derivative of the tangent of a function is equal to secant squared of that function times the derivative of that function, in other words, if ${f(x) = tan(x)}$, then ${f'(x) = sec^2(x)\cdot D_x(x)}$
The derivative of the linear function is equal to $1$
$\sec\left(x+1\right)^2$
Final answer to the problem
$\sec\left(x+1\right)^2$
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