Solve Calculus Problem: f'(x)g'(x) = xf'(x)+f(x) | 10th Fri

  • Thread starter unrealplayer
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    Calculus
In summary, Use the definition of a derivative to prove that the derivative of g(x) is equal to xf'(x) + f(x)(xf prime of x plus f of x). This can be done by applying the definition directly to the function g(x). The answer was found/gotten correctly.
  • #1
unrealplayer
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0
If you can work this out please try and reply to it before friday the 10th!



#1: If f is a differentiable function and g(x) = xf(x), use the
definition of a derivative to show that g'(x)(g prime of x) =
xf'(x)+f(x)(xf prime of x plus f of x).

Definition of a Derivative:

The Derivative of a function f at a number a, denoted by
f'(a) (f prime of a), is:

Lim f(a + h) - f(a)
x -> 0 --------------
h​
 
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  • #2
Apply the definition directly to g(x).
 
  • #3
Thanks a lot, I found/got the right answer
 

1. What is the meaning of f'(x)g'(x)?

In calculus, f'(x)g'(x) represents the derivative of the product of two functions, f(x) and g(x). This means that it is the slope of the tangent line at any point on the curve formed by multiplying the two functions together.

2. How do you solve a calculus problem with f'(x)g'(x) = xf'(x)+f(x)?

This equation is known as the product rule in calculus and can be solved by using the formula: (f*g)' = f'g + fg', where f' and g' represent the derivatives of f(x) and g(x) respectively.

3. What is the significance of the equal sign in the equation f'(x)g'(x) = xf'(x)+f(x)?

The equal sign in this equation signifies that the slope of the tangent line at any point on the curve formed by the product of f(x) and g(x) is equal to the sum of the slopes of the tangent lines at the same point on the individual curves of f(x) and g(x).

4. How is this calculus problem related to the 10th Fri?

The 10th Fri is most likely a specific date or day of the week, which is unrelated to the calculus problem at hand. The problem itself can be solved at any time or on any day.

5. Can this calculus problem be applied to real-life situations?

Yes, the product rule in calculus is often used in physics, economics, and other fields to calculate rates of change or to find the optimal value for a given function. It has many practical applications in various industries and can be used to solve real-life problems.

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