March 20th, 2012, 11:47 PM  #1 
Member Joined: Feb 2012 Posts: 44 Thanks: 0  2nd, 3rd and 4th derivatives
My attempt at calculating these: a) d^2/(dx^2): ln(x+1) b) d^3/(dx^3): x^7 + 4x^6  x^2 c) d^2/(dx^2): 1/(x + 1) d) d^4/(dx^4): cos(2x) a) Product rule: 1/x(x + 1) + ln(1)= 1 + 1/x + ln Linearity rule: (1/x^2) + 1/x b) Linearity rule: 7x^6 + 6x^4  2x= 6(7x)^5 + 4(6x)^3  2= (5)(6)(7x)^4 + (3)(4)(6x)^2 = 210x^4 + 72x^2 c) Quotient rule: ((0)(x + 1)  (1)(1))/(x + 1)^2= 1/(x + 1)^2= ((0)(x+1)^2  (1)2(x + 1))/[(x + 1)^2]^2= (2x  2)/(x + 1)^4 d) the answer ends up being: cos(2x) + sin(2) I think Do these look valid? 
March 21st, 2012, 12:13 AM  #2 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 520 Math Focus: Calculus/ODEs  Re: 2nd, 3rd and 4th derivatives
a) b) c) d) 

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2nd, 3rd, 4th, derivatives 
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