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.

13,401 questions

17,804 answers

1,438 comments

43,436 users

Use the Product Rule to compute the derivative

+1 vote

(d/dx)((X^2+1)(X+9)) | X=13?

asked Jan 31, 2013 in CALCULUS by anonymous Apprentice

2 Answers

+1 vote

Let y = (x2 + 1)(x + 9)

y' = (d/dx)(x2 + 1)(x + 9)

Recall the product rule: (d/dx)(UV) = U' V + U V'

y' = (x2 + 1)' (x + 9) + (x2 + 1)(x + 9)'

General derivative formula: (d/dx)(xn) = nxn-1 and The Derivative of a Constant is 0

y' = (2x + 0)(x + 9) + (x2 + 1)(1+0)

y' = (2x)(x + 9) + (x2 + 1)

y' = 2x2 + 18x + x2 + 1

y' = 3x2 + 18x + 1

 

If x = 13 ?

y' = 3(13)2 + 18(13) + 1

y' = 3(169) + 234 + 1

y' = 507 + 235

y' = 742

answered Jan 31, 2013 by richardson Scholar
0 votes
Let y=(x^2+1)(x+9) y = (x^2)(x) +(x^2)(9) +1(x) + 1(9) y = x^3 + 9x^2 + x + 9 Differentiate with respect to x each side dy/dx = d/dx(x^3) + d/dx(9x^2) + d/dx(x) + d/dx(9) Recall : d/dx(x^n) = n*x^n-1 dy/dx = 3x^3-1 + 9*2x^2-1 + 1 +0 dy/dx = 3x^2 + 18x + 1 If x = 13 dy/dx = 3(13)^2 + 18(13) +1 dy/dx = 3(169) + 234 +1 dy/dx = 507 + 235 dy/dx = 742
answered May 13, 2013 by jeevitha Novice

Related questions

asked Oct 10, 2014 in PRECALCULUS by anonymous
asked Apr 30, 2015 in CALCULUS by anonymous
asked Feb 19, 2015 in CALCULUS by anonymous
...