I'm trying to find the equation of the line tangent to the curve of y=ln(sqrt(7x^2+9)) at x=1.

So I need to find the first derivative:

y'= 7x/(7x^2+9) and at x=1 I find y= 16 (1,16)

Because y= (approx.) 2.77 at x=1 I have a point to substitute in my equation of the line:

y=16x+b

and I find b= -16.23 (approx.)

then the equation of my tangent line at 1 is y=16x-13.23

except that looks nothing like the tangent line on my graph. Where am I off (way off??)