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ChrisV

  • 2 years ago

Find the derivative of the trigonometric function. y=2xsinx+x^2cosx

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  1. Diyadiya
    • 2 years ago
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    \[y'=\frac{d}{dx}(2xsinx)+ \frac{d}{dx}x^2cosx \]

  2. cwrw238
    • 2 years ago
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    use product rule

  3. ChrisV
    • 2 years ago
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    product rule for addition?

  4. Diyadiya
    • 2 years ago
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    use product rule for each term

  5. ChrisV
    • 2 years ago
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    ah ok

  6. cwrw238
    • 2 years ago
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    no - apply product rule to each of the two terms - looks like diyad is doing that now

  7. Diyadiya
    • 2 years ago
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    First do \( \frac{d}{dx}(2xsinx) \) & then \( \frac{d}{dx}(x^2cosx) \)

  8. Diyadiya
    • 2 years ago
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    do you know how to do derivative of 2xsinx ?

  9. cwrw238
    • 2 years ago
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    d (uv)dx = u* dv/dx + v* du/dx where u and v are function of x

  10. ChrisV
    • 2 years ago
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    so

  11. ChrisV
    • 2 years ago
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    2xsix+x^2cosx=2sinx+3xcosx+2xcosx-x^2sinx

  12. ChrisV
    • 2 years ago
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    2sinx oops

  13. Diyadiya
    • 2 years ago
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    Nope

  14. ChrisV
    • 2 years ago
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    2xsinx

  15. ChrisV
    • 2 years ago
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    4xcosx+2sinx-x^2sinx

  16. ChrisV
    • 2 years ago
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    4xcosx+sinx(2-x^2)

  17. ChrisV
    • 2 years ago
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    i mistyped a bunch at first lol

  18. Diyadiya
    • 2 years ago
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    \[\frac{d}{dx} (2xsinx)= 2 \frac{d}{dx}(xsinx) =2[x \frac{d}{dx}sinx+sinx \frac{d}{dx}x]\]

  19. ChrisV
    • 2 years ago
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    my last answer is correct

  20. ChrisV
    • 2 years ago
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    4xcosx+sinx(2-x^2)

  21. ChrisV
    • 2 years ago
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    atleast thats what the books says in the back.

  22. Diyadiya
    • 2 years ago
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    \[ \frac{d}{dx}(2xsinx)=2[xcosx+sinx]\]

  23. ChrisV
    • 2 years ago
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    y=2xsinx+x^2cosx = 2sinx+2xcosx+2xcosx-x^2sinx = 4xcosx +2sinx - x^2sinx = 4xcosx + sinx(2-x^2)

  24. cwrw238
    • 2 years ago
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    thats correct ChrisV

  25. ChrisV
    • 2 years ago
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    thanks guys

  26. Diyadiya
    • 2 years ago
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    oh sorry i thought you were taling about the derivative of 2xsinx

  27. ChrisV
    • 2 years ago
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    did not know i could use product rule on both sides

  28. ChrisV
    • 2 years ago
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    better to learn than wonder :)

  29. cwrw238
    • 2 years ago
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    yep - whenever you have a product of two functions the rule applies

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