Question

Find the equation of the tangent line to y = 3^(x^2 -6x +5) at x=2

I believe y' should be 3^(x^2 -6x +5)(ln(3)), but I have no idea how to proceed from there.

Answer 1

\[y = 3^{x ^{2}-6x+5}\]

Answer 2

\[y' = 3^{x ^{2}-6x+5}\ln(3)\]

Answer 3

\[lny=\ln3^{x ^{2}-6x+5}\]

\[y'/y=(x ^{2}-6x+5)ln3\]

Answer 4

then I think you find the derivative inside and then use the product rule, then divide both sides by y

Answer 5

does that make sense?