SOLUTION: Differentiate: y = x^3 - 2x^2 / cubic root x^2 What I have done: y = x^3 - 2x^2 / x^2/3 dy/dx = x^2/3 (3x^2 - 4x) - (x^3 - 2x^2) (2/3x^-1/3) = 3x^8/3 - 4x^5/3

SOLUTION: Differentiate: y = x^3 - 2x^2 / cubic root x^2 What I have done: y = x^3 - 2x^2 / x^2/3 dy/dx = x^2/3 (3x^2 - 4x) - (x^3 - 2x^2) (2/3x^-1/3) = 3x^8/3 - 4x^5/3 - 2/

Question 696809: Differentiate:
y = x^3 - 2x^2 / cubic root x^2
What I have done:
y = x^3 - 2x^2 / x^2/3
dy/dx
= x^2/3 (3x^2 - 4x) - (x^3 - 2x^2) (2/3x^-1/3)
= 3x^8/3 - 4x^5/3 - 2/3x^8/3 + 4/3x^-2/3 / x^4/3
= 7/3x - 4x^5/3 + 4/3x^-2/3 / x^4/3
= 7/3x^-1/3 - 4x^1/3 + 4/3x^-2
Is my answer correct? Please let me know within 2 days as I have exam and I am unable to visit my teachers / classmates for help. Thanks!
Answer by Edwin McCravy(20056) (Show Source): You can put this solution on YOUR website!




Change the cube root to a fraction exponent:



Change the denominator to a multiplication by a
negative exponential: 

 

Distribute by adding exponents:



Get LCD's of fraction exponents

 

Do the addition of the fraction exponents:



Now we can just use the basic power rule to
find the derivative:



You can either leave it like that or factor out  



Change the exponent  to 1 and the fractional exponential
to a cube root:



I'm sure you can skip some of those steps.  I just broke it down 
all the way just in case.

Edwin

RELATED QUESTIONS
y=(x^3... (answered by ewatrrr)

sopve the differential equation : (x^2-y^2)*dy=2xy*dx 1. dy*6x+dy(-y^2)=2x^2yd 2. (answered by kekegeter ,robertb)

Find f’(t) for f(x) = (3x-4) (4x^3 - x^2 + 1) Find f’(t) for f(x) = x/(4x-6) (answered by greenestamps)

∫(3x^2-2)(x^3-2x)^5... (answered by ewatrrr)

(2x^3-4x^2+3)+(x^3-3x^2+1) (answered by user_dude2008)

Y=|3/2x+2| Y=-|x-3| Y=2|x+2|-3... (answered by tommyt3rd)

(x^3-3x^2+3x-1)�(x^3-2x^2) (answered by tommyt3rd)

Find dy/dx for x^3+2xy^2 = sin... (answered by ikleyn,Edwin McCravy)

1) Let f(t)=(t^2+6t+4)(2t^2+5) f'(t)= f'(2)= 2) f(x)=4x / √8x2+5x−5. (answered by solver91311)