Question

Find the equation of the tangent to y = 2^(2x) - (ln 4)x + 2ln(x +1) when x=0

Answer 1

Find the y coordinate on the original graph when x = 0
(sub into y = 2^(2x) - (ln 4)x + 2ln(x +1)),
and that point corresponds to the point on the graph (x1,y1)
Now take the derivative of y = 2^(2x) - (ln 4)x + 2ln(x +1), to find y'
And sub in x =0, to find the slope of the tangent (m) at the point x = 0.

Now with all the information you have, you can substitute your values in the line equation:
y-y1 = m(x -x1), to find the equation of your tangent