How can I find the derivative of an integration with respect to y?

In summary, the derivative of an integration is the inverse operation of integration and involves finding the rate of change of a function at a specific point. To find the derivative of an integration, you need to first identify the function being integrated and use derivative rules to differentiate it, then integrate the resulting function. Integration and differentiation are inverse operations and have various real-life applications, such as in physics, economics, and engineering. The chain rule can also be used to find the derivative of an integration, particularly when dealing with nested or composite functions.
  • #1
phonic
28
0
Dear all,

I have a function in the form of [itex]f(y) = \int_{-h(y)}^{h(y)} g(x,y)dx [/itex] . Then how to calculate its derivative w.r.t. y? i.e.
[itex] \frac{d f(y)}{dy} [/itex]

Thank you very much for your input!
 
Physics news on Phys.org

FAQ: How can I find the derivative of an integration with respect to y?

What is the derivative of an integration?

The derivative of an integration is the inverse operation of integration. It is a mathematical process that involves finding the rate of change of a function at a specific point.

How do you find the derivative of an integration?

To find the derivative of an integration, you need to first identify the function that is being integrated and use the power rule or other derivative rules to differentiate it. Then, you can integrate the resulting function to get the original function.

What is the relationship between integration and differentiation?

The relationship between integration and differentiation is that they are inverse operations of each other. Integration involves finding the area under a curve, while differentiation involves finding the rate of change of a function.

Can you use the chain rule to find the derivative of an integration?

Yes, the chain rule can be used to find the derivative of an integration. It is a useful method when the integrand involves nested functions or composite functions.

What are some real-life applications of the derivative of an integration?

The derivative of an integration has various real-life applications, such as in physics to calculate velocity and acceleration, in economics to determine marginal cost and revenue, and in engineering to analyze rates of change in systems, among others.

Similar threads

I The Euler-Lagrange equation and the Beltrami identity
Replies
1
Views
2K
I Is My Calculus of Variations Approach Correct?
Replies
12
Views
2K
I Partial derivatives of the function f(x,y)
Replies
6
Views
2K
B Why is this definite integral a single number?
Replies
20
Views
3K
MHB How to find F(x,y) for $f(x,y)= h(y)\hat{i} + g(x)\hat{j}?$
Replies
11
Views
2K
A Double integral with infinite limits
Replies
11
Views
2K
I From a proof on directional derivatives
Replies
9
Views
2K
I How to manipulate functions that are not explicitly given?
Replies
16
Views
1K
I Why the integral of a differential does not give the function back in 2D?
Replies
14
Views
2K
I Derivative of a function is equal to zero
Replies
4
Views
2K

Hot Threads

Recent Insights

Back
Top