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Find (dy)/(dx) in the following: (...

Find `(dy)/(dx)` in the following: (a)`x^3+x^2y+x y^2+y^3=81` (b) `xy+y^2 =tan x+ y ` (c) `x^2 + xy+ y^2 = 100`

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BANSAL-LIMITS AND DERIVATIVES-All Questions
  1. If x y+y^2=tanx+y ,t h e nfin d(dy)/(dx)dot

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  2. Find (dy)/(dx) in the following: x^2+x y+y^2=100

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  3. Find (dy)/(dx) in the following: (a)x^3+x^2y+x y^2+y^3=81 (b) x...

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  4. Find (dy)/(dx) in the following: sin^2y+cosx y=pi

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  5. Find (dy)/(dx) of x^2+x y+cos^2y=1

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  6. Find (dy)/(dx) of y+siny=cosx

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  7. Find the derivative of (sinx)^(sinx),\ \ 0<x<pi .

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  8. Differentiate w.r.t. x the function (sinx-cosx)^((sinx-cosx)),pi/4<x<...

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  9. Differentiate w.r.t. x the function x^x+x^a+a^x+a^a , for some fixe...

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  10. Find the derivative of x^x^(2-3)+(x-3)^x^2 , for x >3

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  11. Find the derivatives w.r.t. x (i) log(e^x((x-2)/(x+2))^(3/4))

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  12. If y=f(x)=x^3+x^5 and g is the inverse of f find g^(prime)(2)

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  13. Let f(x) = exp(x^3 +x^2+x) for any real number and let g(x) be the inv...

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  14. If g is the inverse of f and f'(x)=1/(1+x^n) , prove that g^(prime)(x)...

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  15. Prove that derivative of sec^(-1)x is 1/(|x|sqrt(x^2-1)) if |x|>1 , us...

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  16. Find (dy)/(dx) for y=tan^(-1){(1-cosx)/(sinx)},-piltxltpi

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  17. D(tan^(-1)x+tan^(-1)(1/x))=

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  18. If y=(tan^(-1)x-cot^(-1)x)/(tan^(-1)x+cot^(-1)x) , find ((dy)/(dx)])(x...

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  19. If y=tan^(-1)((sqrt(1+x)-sqrt(1-x))/(sqrt(1+x)+sqrt(1-x))), find (dy)/...

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  20. Solve y=tan^(-1)((sqrt(1+x^2)-1)/x)

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