- #1
Martin Harris
- 103
- 6
Hello, and thank you for your time.
I just started my A-levels derivatives/differentiation , and I would be more than happy if you could help me clarify it.
For example I know that y is a function in terms of x right?
y=f(x)
The derivative of it is f'(x)=dy/dx .
This means it is the rate of change of y over the rate of change of x,which is also called gradient.
What is the actual difference between a function and its derivative?What is the physical meaning of that?
Let's take an example.
For the Circle:
Let's say Area ##A=\pi*r^2##
then if we derivate it with respect to r it becomes:
##\frac{dA}{dr}####=####2*\pi*r##
Which is the circumference of the circle.
What it is the meaning of this derivative?It is the rate of change of A with respect to r.
But what does it mean ?I know that 2*pi*r it's the circumference of the circle.
Another question I have it is regarding the difference between the derivative and differentiation.
Is it right if I say
Derivative=rate of change of y with respect to y
Differentiation=find out derivative of a function.
What exactly is the difference between those 2?
I am trying to understand the physical meaning, the phenomena behind all those derivatives/differentiation problems.
Also,what about this, I know that dy/dx is the gradient,rate of change.
but I also learned that a small change can occur in the gradient which is δy/δx
we know that dy/dx~δy/δx
but what exactly is the relation between dy/dx and δy/δx?
How can δy/δx be interpreted in terms of dy/dx?
I mean I was thinking of something like ##\frac{δy}{δx}##=##\frac{y+δy}{x+δx}##
Thank you very much in advance,it is much appreciated.
I just started my A-levels derivatives/differentiation , and I would be more than happy if you could help me clarify it.
For example I know that y is a function in terms of x right?
y=f(x)
The derivative of it is f'(x)=dy/dx .
This means it is the rate of change of y over the rate of change of x,which is also called gradient.
What is the actual difference between a function and its derivative?What is the physical meaning of that?
Let's take an example.
For the Circle:
Let's say Area ##A=\pi*r^2##
then if we derivate it with respect to r it becomes:
##\frac{dA}{dr}####=####2*\pi*r##
Which is the circumference of the circle.
What it is the meaning of this derivative?It is the rate of change of A with respect to r.
But what does it mean ?I know that 2*pi*r it's the circumference of the circle.
Another question I have it is regarding the difference between the derivative and differentiation.
Is it right if I say
Derivative=rate of change of y with respect to y
Differentiation=find out derivative of a function.
What exactly is the difference between those 2?
I am trying to understand the physical meaning, the phenomena behind all those derivatives/differentiation problems.
Also,what about this, I know that dy/dx is the gradient,rate of change.
but I also learned that a small change can occur in the gradient which is δy/δx
we know that dy/dx~δy/δx
but what exactly is the relation between dy/dx and δy/δx?
How can δy/δx be interpreted in terms of dy/dx?
I mean I was thinking of something like ##\frac{δy}{δx}##=##\frac{y+δy}{x+δx}##
Thank you very much in advance,it is much appreciated.
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