first and second derivative
in Calculus Answers by Level 1 User (120 points)

Your answer

Your name to display (optional):
Privacy: Your email address will only be used for sending these notifications.
Anti-spam verification:
To avoid this verification in future, please log in or register.

1 Answer


Let u=(x2+10)2, then du/dx=4x(x2+10), d2u/dx2=4(x2+10)+8x2=4(3x2+10); let v=x-10, then dv/dx=1, d2v/dx2=0.

h=uv, dh/dx=udv/dx+vdu/dx=(x2+10)2+4x(x-10)(x2+10).

Expanding: dh/dx=x4+20x2+100+4x(x3+10x-10x2-100),

dh/dx=5x4-40x3+60x2-400x+100, the first derivative, d2h/dx2=20x3-120x2+120x-400, the second derivative.



d2h/dx2=20x3-120x2+120x-400, which confirms the above calculation of the second derivative.

by Top Rated User (894k points)

Related questions

1 answer
1 answer
asked May 22, 2013 in Calculus Answers by anonymous | 291 views
1 answer
asked Mar 26, 2013 in Calculus Answers by anonymous | 402 views
Welcome to, where students, teachers and math enthusiasts can ask and answer any math question. Get help and answers to any math problem including algebra, trigonometry, geometry, calculus, trigonometry, fractions, solving expression, simplifying expressions and more. Get answers to math questions. Help is always 100% free!
86,882 questions
93,634 answers
24,243 users