anonymous
  • anonymous
Can someone help me with derivatives and chain rule... Find derivative of (t^3 + 1 )^(100) sqrt(1-x^2)
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
\[(t ^{3} + 1)^{100}\]
anonymous
  • anonymous
\[\sqrt{1-x ^{2}}\]
anonymous
  • anonymous
So you first multiply everything on the inside of the parenthesis by 100 for the top equation and raise it to 100-1...Then you multiply all of that by the derivative of everything inside the parenthesis

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anonymous
  • anonymous
so it would be \[100(t ^{2}+1)^{99} x 2t\]
anonymous
  • anonymous
\[100t ^{3} + 100\]
anonymous
  • anonymous
where did you get x2t?
anonymous
  • anonymous
x is multiplying- 2t is the derivative of what is inside the parenthesis
anonymous
  • anonymous
can you explain how you got the derivative of the inside parenthesis adn explain about x
anonymous
  • anonymous
Sorry, there is no x- i just used x to imply multiplication. The derivative of the inside is the derivative of t^2 which is 2t plus the derivative of 1 which is 0
anonymous
  • anonymous
Oh ok so when you multiply through what do you get?
anonymous
  • anonymous
200t(t ^{2}+1)^{99}
anonymous
  • anonymous
\[200t(t ^{2}+1)^{99}\]
anonymous
  • anonymous
I kept getting online \[300t^2(t^3 +1) ^(99)\]
anonymous
  • anonymous
that is raised to 99
anonymous
  • anonymous
Ah crap- i saw t^2 instead of t^3---that would be right then
anonymous
  • anonymous
ok cool... what about the second one
anonymous
  • anonymous
and how again did you get 2t as the inside derivative

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