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If x= cos theta, y= sin^3theta, show tha...

If x= cos `theta`, y= `sin^3``theta`, show that y (`d^2` y)/(d`x^2`) + `(dy/dx)^2` = 3 `sin^2``theta`(5 `cos^2``theta` - 1)

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CHETANA PUBLICATION-Differentiation-Exercise
  1. If x= a cos theta, y= b sin theta, show that a^2[y (d^2 y)/(dx^2) +(dy...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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  19. If y= 1- cos theta, x= 1- sin theta, then dy/dx at theta = pi /4 is......

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  20. If sec(frac{x+y}{x-y}) = a^2, then (d^2 y)/(dx^2) = ............ A) y...

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