Determine the equation of the tangent line to fx x22x12 at

Question

Question 1) Find the y' for the following equations-

(a) y = (12x2 - 1)²e^2x

(b) y = (ln(x³ + 4x))^1/3

(c) y = (2x³+1)/(e^x2)

(d) y = x2e2x + (ln(x²+3x-3))/(3x)

Question 2) Find the y' For x²y + 4(2 - y2)^2.5 = 5y² - 5.

Question 3) If y = 4t² - 2t;   t = ln x. Find dy/dx at x = 2.

Question 4) Determine the equation of the tangent line to f(x) = x²(2x+1)² at x =1.