How do you find derivatives and what do they represent in calculus?

[Mol_Bolom]

I think I finally figured out derivitaves, but not sure...

The derivative/differential of x in
x is 1
3x + 5 is 3
5x^2 - 2 is 10

And breaking down a quadratic thus

3x^5 + 2x^3 + 5x - 1
The first derivative is 15x^4 + 6x^2
The second derivative is 60x^3 + 12x
Third 180x^2
Fourth 360x
And final 360.

 

[Werg22]

3x^5 + 2x^3 + 5x - 1
The first derivative is 15x^4 + 6x^2
The second derivative is 60x^3 + 12x
Third 180x^2
Fourth 360x
And final 360.

No, first and third are wrong.

1. 15x^4 + 6x^2 + 5
2. 60x^3 + 12x
3. 180x^2 + 12
4. 360x
5. 360

 

[uman]

The derivative of $$5x^2-2$$ is actually $$10x$$.

 

[Mol_Bolom]

Ah...That was the area I had a problem with...The final solitary number...
Wado (thanks)

 

[HallsofIvy]

I think I finally figured out derivitaves, but not sure...

The derivative/differential of x in
x is 1
3x + 5 is 3
5x^2 - 2 is 10

The derivative (not differential) of 5x²- 2 at at x= 1 is 10. More generally, the derivative of 5x²- 2 at any x is 10x. The differential of x is dx, the differential fo 3x+ 5 is 3dx and the differential of 5x²- 2 is 10x dx.

And breaking down a quadratic thus

3x^5 + 2x^3 + 5x - 1
The first derivative is 15x^4 + 6x^2

The first derivative is 15x⁴+ 6x²+ 5

The second derivative is 60x^3 + 12x
Third 180x^2
Fourth 360x
And final 360.

Well, I wouldn't call it "final". That's the fourth derivative. The fifth derivative, and all succeeding derivatives is 0.

 

[ice109]

The derivative (not differential) of 5x²- 2 at at x= 1 is 10. More generally, the derivative of 5x²- 2 at any x is 10x. The differential of x is dx, the differential fo 3x+ 5 is 3dx and the differential of 5x²- 2 is 10x dx.

don't you mean the differential of y?

isn't the differential of x : dx?

 

[sutupidmath]

don't you mean the differential of y?

I don't see any
y's in there. It can be any variable expressed as a function of x.

isn't the differential of x : dx?

I think this is what Halls said also!

 

[ice109]

woops