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DLS

  • 3 years ago

Please find the derivative c:

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  1. DLS
    • 3 years ago
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    \[y=(3x^2+6x+5)^{(7/2)} \]

  2. cwrw238
    • 3 years ago
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    use the chain rule ley u = 3x^2 + 6x + 5 , then y = u^(7/2) find du/dx and dy/du then dy/dx = dy/du * du/dx

  3. DLS
    • 3 years ago
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    I did the same.

  4. cwrw238
    • 3 years ago
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    ok - and what did you get?

  5. cwrw238
    • 3 years ago
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    7/2(3x^2 + 6x + 5)^(5/2) * (6x +6)

  6. DLS
    • 3 years ago
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    Im little confused.. Will it be like this? \[y=\frac{(3x^{2}+6x+5)^{7/2}}{d(6x+5)} \times \frac{d(6x+5)}{d5} \] something like this? perhaps confused..

  7. cwrw238
    • 3 years ago
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    y = u^(7/2) dy/du = (7/2) u^(7/2 - 1) = (7/2) u^(5/2) substituting back for u dy/du = (7/2) ( 3x^2 + 6x + 5)^(5/2) du/dx = 6x + 6 now multiply the two results together gives (7/2)(6x+6)(3x^2 + 6x + 5)^(5/2)

  8. cwrw238
    • 3 years ago
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    with practice you won't need to do the substitution u

  9. DLS
    • 3 years ago
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    how did u get 6x+6

  10. cwrw238
    • 3 years ago
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    6x + 6 is the derivative of 3x^2 + 6x + 5 the du/dx in the above post

  11. DLS
    • 3 years ago
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    thanks!

  12. cwrw238
    • 3 years ago
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    you use chain rule when you have a 'function of a function' like this one 3x^2 +6x + 5 is the 'inside' function of (3x^2 +6x + 5)^7/2

  13. cwrw238
    • 3 years ago
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    yw

  14. DLS
    • 3 years ago
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    i have some more questions im confused with!

  15. cwrw238
    • 3 years ago
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    i'm sorry but i must go now

  16. DLS
    • 3 years ago
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    okay..

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