Math- Geometry Please SOlve

[Guest]

Please Solve this, I am unable.

Please also solve this :

Let f(x), g(x) and h(x) be the functions from Problem A.1. Find the derivative λ0(x) of the following function with respect to x:

λ(x) = f(x) · g(x) + f(x) · h(x) − g(x) · h(x)


Note: here problem A.1 is the upper problem.


Please solve both the problem.​

[Guest]

f(x) and h(x) are linear functions- their graphs are straight lines and their derivatives are constants, the slopes of those lines. f is a straight line from (2, 0) to (4, 2). What is it slope (derivative)? h is a straight line from (8, 2) to (10, 4). What is it slope (derivative)?

g is the upper semi- circle with center at (6, 2) and radius 2. The equation of the entire circle would be [tex](x- 6)^2+ (y- 2)^2= 4[/tex]. [tex](y- 2)^2= 2- (x- 6)^2[/tex] so the upper semis circle is given by [tex]y- 2= \sqrt{2- (x- 6)^2}[/tex] or [tex]y= 2+ (12x- x^2- 34)^{1/2}[/tex]. What is the derivative of that?