## newatcalculus 4 years ago What is the derivative of 5x^2 + 10x + 5? I'm new at calculus

1. roshan2004

10x+10

2. AntiMatter

here you can apply the power rule

3. misterf

When you are deriving polynomials, the important thing to remember is that you can derive each piece independently.

4. AntiMatter

\[ 3x^3 + 5x + 10\] To find the first derivative you can apply the Power Rule For Example, in general, finding the derivative of a function with exponents follows such a pattern: \[x^{n} = n*x^{n-1}\] Turn the exponent into a coefficient and then subtract 1 from the exponent for the first derivative

5. roshan2004

Differentiate each terms

6. AntiMatter

so you use that with misterf's idea, and work through each part of the function individually

7. misterf

very nice, antimatter. you can do that to each x term and then add them back together

8. newatcalculus

What is a derivative? What does it represent?

9. AntiMatter

ha, right!

10. misterf

it is the rate of change of function at a given value.

11. roshan2004

Derivative is like a function

12. roshan2004

which gives us the rate of change

In the physical world, for example, if you have a graph that shows the position of something, the derivative of that graph at a given point is the speed of the object at that point.

14. misterf

say your function represents your distance over time. if you take the derivative of that function, you will get a function for your speed.

15. roshan2004

of the function with respect to any independent variable

Likewise, if you have a graph (or function) describing the speed, the derivative at a given point gives you the acceleration at that point, i.e., the rate at which your speed is changing. Your speed is the rate at which your position is changing. Etc.

17. shameer

10x+10

18. myininaya

by the way derive is different from differentiate

19. myininaya

derive means sort of like to find differentiate means to take the derivative

20. shameer

i think its very easy and simple method to find derivate