- #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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