anonymous
  • anonymous
derivatieve of x^2 secy assuming that the equation determines a differentiable function f suht that y= f(x)
Mathematics
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anonymous
  • anonymous
derivatieve of x^2 secy assuming that the equation determines a differentiable function f suht that y= f(x)
Mathematics
schrodinger
  • schrodinger
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anonymous
  • anonymous
technically cant be done
anonymous
  • anonymous
it has to equal something
anonymous
  • anonymous
x^2 secy must equal something

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anonymous
  • anonymous
= y^2 +1
anonymous
  • anonymous
x^2 (cosy)^-1 = y^2 +1
anonymous
  • anonymous
rewritting sec as cos^-1
anonymous
  • anonymous
oh i used the product rule
anonymous
  • anonymous
yeh, it is correct
anonymous
  • anonymous
(2x)(secy) but i dont know whts goes in the next bracket
anonymous
  • anonymous
because y depends on x , x^2 (cosy)^-1 needs to be differenitated as product
anonymous
  • anonymous
secytany(x^2)y'
anonymous
  • anonymous
so then it'll be 2yy' = 2xsecy+x^2secytany*y'
anonymous
  • anonymous
so LHS: let u= x^2 du/dx = 2x v= (cos(y))^-1 dv/dx = -1 ( cos(y) )^-2 * -sin(y) (dy/dx)
anonymous
  • anonymous
so the LHS = 2x (cosy)^-1 +(x^2sin(y) (sec(y))^2 ) dy/dx
anonymous
  • anonymous
and the RHS will equal 2y dy/dx
anonymous
  • anonymous
\[2xsec(y) +x^2\sin(y)\sec^2(y)\frac{dy}{dx} = 2y \frac{dy}{dx}\]
anonymous
  • anonymous
solve for the dy/dx
anonymous
  • anonymous
ok i understand thank you so much

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