Derivative Notation

[nycmathguy]

Derivative Notation

The derivative of y is y'. Yes? Thus means y prime. Yes?

The derivative of f(x) = f'(x). Yes? This means f prime of y. Yes?

What about dy/dx? Does this mean the derivative of y with respect to x?

What does d/dx mean?

Can dy/dx be expressed as df(x)/dx?

Any other way to represent the derivative?

 

[MathLover1]

Yes. y'(x) means y prime of x. Prime means the derivative.
dx/dy also means the derivative.
It's just different ways of writing same thing.
dy/dx = df(x)/dx.......remember that f(x)=y

 

[nycmathguy]

Yes. y'(x) means y prime of x. Prime means the derivative.
dx/dy also means the derivative.
It's just different ways of writing same thing.
dy/dx = df(x)/dx.......remember that f(x)=y

I like dy/dx, y prime and f prime of x.
What d/dx mean?

 

[MathLover1]

d/dx is differentiating something that isn't necessarily an equation denoted by y.
dy/dx is differentiating an equation y with respect to x
dy/dx is a noun. It is the thing you get after taking the derivative of y.
d/dx is a verb. It says "take the derivative of this thing I'm about to write after this"

 

[nycmathguy]

d/dx is differentiating something that isn't necessarily an equation denoted by y.
dy/dx is differentiating an equation y with respect to x
dy/dx is a noun. It is the thing you get after taking the derivative of y.
d/dx is a verb. It says "take the derivative of this thing I'm about to write after this"

My example:

Find derivative of 2x^2 + 5x.

d/dx [2x^2] + d/dx [5x]

Answer: 4x + 5 is the slope.

Can you give me an example using dy/dx?

 

[MathLover1]

Answer: 4x + 5 is the tangent line which has a slope=4

y=2x^2 + 5x->using dy/dx

 

[nycmathguy]

Answer: 4x + 5 is the tangent line which has a slope=4

y=2x^2 + 5x->using dy/dx

So, using dy/dx, we dy/dx = 4x + 5.

Another example.

Find derivative of y.

So, d/dx [y] = dy/dx = y prime.

 

[MathLover1]

yes

We denote derivative by dy/dx, the change in y with respect to x.

If y(x) is a function, the derivative is represented as y’(x)
dy/dx=y’(x)

 

[nycmathguy]

yes

We denote derivative by dy/dx, the change in y with respect to x.

If y(x) is a function, the derivative is represented as y’(x)
dy/dx=y’(x)

What would be dx/dy?

 

[MathLover1]

What would be dx/dy?

 

[nycmathguy]

What would be dx/dy?

View attachment 3373

Are you say that the derivative of x is d/dy [x], which is dx/dy?

I always thought that the derivative any variable is 1.
No?

Derivative of x = 1.

Derivative of y = 1.

Derivative of z = 1.

No?

 

[MathLover1]

dx/dy is just derivative of inverse function
if function is y(x) inverse is x(y)

 

[nycmathguy]

dx/dy is just derivative of inverse function
if function is y(x) inverse is x(y)

Ok.