I found some questions in which i have doubts. Please answer in detail along with diagram or graph where needed.

And first question that i pointed with black circle, please give detailed explanation along with diagram or graph and include examples so that it will be easy for me to learn.

And in 4th question, please provide solution with graph if possible.

If you provide typing work then it will be much better to learn because sometimes handwriting becomes difficult to learn and understand.

?

Why might one prefer to use the logarithmic differentiation for finding derivatives of functions that have another function as an exponent? 4. Determine if G(z) = (2 - 6) Inz is increasing or decreasing at the following points. (a) z=1 (b) z=5 (c) z=20 7. Find the derivative for the function f(@) = (Vx)" 3. Let pi = (-1,0), p2 = (1,0), and consider the set of all points F = (r, y) such that the sum of the distance between F and p; and the distance between f and pz is a constant k > 2. e.g. IF - pll + If - pill = k (a) Describe the set of points forming the curve F. (b) For k = 4 sketch the curve. 5. Consider f(x,y) = vry at the point P(2,8) moving toward the point Q(5, 4). (a) Find the gradient of f at P (b) Find the directional derivative of f at P in the direction of