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If x= a cos theta, y= b sin theta, show ...

If `x= a cos theta, y= b sin theta`, show that `a^2[y (d^2 y)/(dx^2) +(dy/dx)^2] + b^2 = 0`

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CHETANA PUBLICATION-Differentiation-Exercise
  1. If y= log(x+ sqrt (x^2 + a^2)), show that (x^2 + a^2)(d^2 y)/(dx^2) + ...

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  2. If ax^2 + 2hxy + by^2 =0, show that (d^2 y)/(dx^2) = y/x

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  3. If x= a cos theta, y= b sin theta, show that a^2[y (d^2 y)/(dx^2) +(dy...

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  4. If y= cos (m sin^(-1) x), show that (1- x^2)(d^2 y)/(dx^2) - x(dy/dx) ...

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  5. If x= cos theta, y= sin^3theta, show that y (d^2 y)/(dx^2) + (dy/dx)^2...

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  6. If 2y= sqrt (x+1) + sqrt (x-1), show that 4(x^2 -1) y2 + 4xy1 - y = 0

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  7. Find dy/dx if y= log (frac { x+ sqrt (x^2+a^2) }{sqrt (x^2+a^2) - x ...

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  8. Let f(1)=3, f'(1)= frac{-1}{3}. g(1)=-4, and g'(1) = frac{-8}{3}, The ...

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  9. If y= sec (tan^(-1) (x)), then dy/dx at x=1 is equal to ......... A) ...

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  10. If f(x) = sin^(-1){(frac {4^((x +(1/2)))}{1+ 2^(4x)))}, which of the f...

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  11. If x^y = y^x, then dy/dx = ......... A) frac{y(x log y - y)}{x(y log ...

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  12. If y= sin(2 sin^(-1) x), then dy/dx= ............ A) frac{2-4x^2}{sqr...

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  13. If y= tan^(-1) (frac{x}{1+ sqrt (1 - x^2)}) + sin[ 2tan^(-1) (sqrt ((1...

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  14. If y is a function of x and log(x+y) = 2xy, then the value of y'(0) = ...

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  15. If g is the inverse function of f and f'(x)= frac{1}{1+x^7}, then the ...

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  16. If x sqrt (y+1) + y sqrt (x+1) =0 and x != y then dy/dx=............ A...

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  17. If y= tan^(-1) (sqrt (frac {a-x}{a+x})), where -a < x < a then dy/dx= ...

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  18. If x= a(costheta + sintheta), y= a(sintheta + costheta), then (d^2y)/(...

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  19. If y= a cos(log x) and A ((d^2 y)/(dx^2)) + B (dy/dx) + C = 0 , then ...

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  20. If x^y = e^(x-y), then dy/dx = ............ A) frac{1 + x}{1+ log x} ...

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