SOLUTION: Obtain dy/dx (rate of change) using the direct rule: y= 2.5x^4 - x^3/2.5 - x/2.5 +2.5 & y= (x^3-2.5x^2)/(2.5sqrtx)

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: Obtain dy/dx (rate of change) using the direct rule: y= 2.5x^4 - x^3/2.5 - x/2.5 +2.5 & y= (x^3-2.5x^2)/(2.5sqrtx)      Log On


   



Question 343519: Obtain dy/dx (rate of change) using the direct rule:
y= 2.5x^4 - x^3/2.5 - x/2.5 +2.5
&
y= (x^3-2.5x^2)/(2.5sqrtx)

Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!


I'm unfamiliar with the term "direct rule." For the first function you need repeated application of the power rule (presuming that I am interpreting your rendering correctly)

Power Rule



So:



I'm going to do the second one for you as well because I'm in a good mood. But next time -- READ THE INSTRUCTIONS -- One question per post.

For the second one you need the Quotient Rule and the Power Rule:

Quotient Rule

For:



where

and are both differentiable,



And we want to calculate:



Begin with calculating the derivatives of numerator and denominator separately:



hence



and



So









John

My calculator said it, I believe it, that settles it