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anonymous

  • 5 years ago

derivatieve of x^2 secy assuming that the equation determines a differentiable function f suht that y= f(x)

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  1. anonymous
    • 5 years ago
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    technically cant be done

  2. anonymous
    • 5 years ago
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    it has to equal something

  3. anonymous
    • 5 years ago
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    x^2 secy must equal something

  4. anonymous
    • 5 years ago
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    = y^2 +1

  5. anonymous
    • 5 years ago
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    x^2 (cosy)^-1 = y^2 +1

  6. anonymous
    • 5 years ago
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    rewritting sec as cos^-1

  7. anonymous
    • 5 years ago
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    oh i used the product rule

  8. anonymous
    • 5 years ago
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    yeh, it is correct

  9. anonymous
    • 5 years ago
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    (2x)(secy) but i dont know whts goes in the next bracket

  10. anonymous
    • 5 years ago
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    because y depends on x , x^2 (cosy)^-1 needs to be differenitated as product

  11. anonymous
    • 5 years ago
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    secytany(x^2)y'

  12. anonymous
    • 5 years ago
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    so then it'll be 2yy' = 2xsecy+x^2secytany*y'

  13. anonymous
    • 5 years ago
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    so LHS: let u= x^2 du/dx = 2x v= (cos(y))^-1 dv/dx = -1 ( cos(y) )^-2 * -sin(y) (dy/dx)

  14. anonymous
    • 5 years ago
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    so the LHS = 2x (cosy)^-1 +(x^2sin(y) (sec(y))^2 ) dy/dx

  15. anonymous
    • 5 years ago
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    and the RHS will equal 2y dy/dx

  16. anonymous
    • 5 years ago
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    \[2xsec(y) +x^2\sin(y)\sec^2(y)\frac{dy}{dx} = 2y \frac{dy}{dx}\]

  17. anonymous
    • 5 years ago
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    solve for the dy/dx

  18. anonymous
    • 5 years ago
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    ok i understand thank you so much

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spraguer (Moderator)
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