MHB Derivative of f(x), g(x) and h(x) from Calculus Problem A.1: Solve Urgent"

[sfvdsc]

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.

 

[jonah1]

Beer induced query follows.

View attachment 11486

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.

What have you done so far?

 

[HOI]

That's a pretty straight forward problem. Using the "sum rule", that (f+ g)'= f'+ g', and the "product rule", that (fg)'= f'g+ fg' the derivative of fg+ fh- gh is f'g+ fg'+ f'h+ fh'- g'h- gh'.

You should see immediately that f'= h'= 1. What is g'?

 

[HOI]

f(x)= x- 2. That line segment starts at (2, 0) and ends at (4, 2). What is the length of that line segment?

h(x)= x- 6. That line segment starts at (8, 2) and ends at (10, 6). What is the length of that line segment?

g(x) is a semi-circle with end points (4, 2) and (8, 2). What is its radius? What is its circumference?

 

[Prove It]

Since when is a semicircle a line segment?

 

[HOI]

For this problem it was an honorary line segment!