Fd the equations for the tangent line of the graph fx

Question

Find the derivative of each of the following function:

a. y = cos² (4x)
b. y = √(e^4x +1)
c. y = x^2x.
d. y = 2^{sin x}.

2. Find the second derivative of f(x) = e^{In x}.

3. Performe the implicit differentiation to find the slop of the curve 2x² + 3y² = 5xy at the point (1,1).

4. For the function x² + 4y = 4 with dx /dt = 2 find dy / dt at the point (x,y) = (2,0).

5. Find the equations for the tangent line of the graph f(x) = -x² + 2x at x = 4.