Welcome :: Homework Help and Answers :: Mathskey.com
Welcome to Mathskey.com Question & Answers Community. Ask any math/science homework question and receive answers from other members of the community.

13,435 questions

17,804 answers

1,438 comments

97,198 users

How to differentiate y=(x+1)²(x+2)² and y=4x/√2x

+1 vote
asked Mar 10, 2013 in CALCULUS by potatoes Rookie

1 Answer

0 votes
 
Best answer

y=(x+1)²(x+2)²

Recall the product rule of derivatives,

d/dx(uv)=uv'+vu'

u=(x+1)²

u'=2(x+1)

v=(x+2)²

v'=2(x+2)

dy/dx=(x+1)²*2(x+2)+(x+2)²*2(x+1)

       =2(x+1)(x+2)(x+1+x+2)

        =2(x+1)(x+2)(x+3)

------------------------------

y=4x/√2x

Recall the product rule of derivatives,

d/dx(u/v)=u'v-v'u/v^2

u=4x

u'=4

v=√2x

v'=√2x^3/2

dy/dx=√2x*4-√2x^3/2*4x/2x

        =4√2x(4-x^2)/2x

answered Mar 11, 2013 by bradely Mentor
selected Mar 11, 2013 by potatoes
  • Derivative of the function y  = (x + 1)²(x + 2)² is 2(x + 1)(x + 2)(2x + 3)

 

  • The function image
     

Apply The quotient rule in derivatives

image

Apply derivative on each side with respect of x.

image

image

image

image

Derivative of the function image is image.

 

Related questions

asked May 17, 2014 in CALCULUS by anonymous
asked Jul 22, 2014 in CALCULUS by anonymous
...