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

In summary, the conversation is about finding the derivative of a function involving three functions, f(x), g(x), and h(x), and using the "sum rule" and "product rule" to solve it. The summary also includes additional information about the given functions and calculations mentioned in the conversation.
  • #1
sfvdsc
5
0
Screenshot 2021-11-18 at 7.44.26 AM.png


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.
 
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  • #2
Beer induced query follows.
sfvdsc said:
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?
 
  • #3
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'?
 
  • #4
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?
 
  • #5
Since when is a semicircle a line segment?
 
  • #6
For this problem it was an honorary line segment!
 

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

What is a derivative?

A derivative is a mathematical concept that represents the rate of change of a function at a specific point. It can also be thought of as the slope of the tangent line to the function at that point.

How do you find the derivative of a function?

To find the derivative of a function, you can use the rules of differentiation, such as the power rule, product rule, quotient rule, and chain rule. These rules allow you to find the derivative of a function by manipulating its algebraic expression.

What is the difference between f(x), g(x), and h(x)?

In calculus, f(x), g(x), and h(x) are all examples of functions. The main difference between them is the specific variable or input they represent. For example, f(x) may represent a function of x, while g(t) may represent a function of time.

Why is it important to solve for the derivative?

Finding the derivative of a function is important because it allows us to analyze the behavior of the function and make predictions about its future values. It also helps us to find the maximum and minimum points of a function, which is useful in optimization problems.

What is the urgency in solving Calculus Problem A.1?

The urgency in solving Calculus Problem A.1 may vary depending on the specific context, but in general, solving calculus problems is important for understanding the fundamental principles and techniques of calculus, which are essential for many fields of science and engineering.

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