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If x= a(cos `theta` + sin `theta`), y= a(sin `theta` + cos `theta`), then [(`d^2` y)/(d`x^2`) ] at `theta` = `pi`/4 ............. A) 0 B) 1 C) -1 D) `1/sqrt 2`

A

`frac{8 `sqrt 2}{a`pi`}

B

- `frac{8 `sqrt 2}{a`pi`}

C

`frac{a`pi`}{8 `sqrt 2}

D

`frac{4 `sqrt 2}{a`pi`}

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CHETANA PUBLICATION-Differentiation-Exercise
  1. If x= a(cos t + tsin t), y= a(sin t- t cos t), then dy/dx ...............

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  2. If y= cot^(-1)(frac {1-3x^2}{3x - x^3}), then dy/dx=....... A) frac{3...

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  3. If log (sqrt (x^2 + y^2)) = tan^(-1)(frac{y}{x}), then frac{dy}{dx} is...

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  4. If x= a(t-1/t), y=a(t+1/t), then dy/dx =........ A) x/y B) y/x C) ...

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  5. If x^2 + 6xy + y^2 = 10, then frac{d^2y}{dx^2} =..........

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  6. If e^y = (x+1) then (d^2y)/(dx^2) =.......... A) (dy/dx)^2 B) -(dy/dx)...

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  7. If x= a(cos theta + sin theta), y= a(sin theta + cos theta), then [(d^...

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

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

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  10. If y= cos(x^2 + a^2) find dy/dx

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  11. Differentiate tan^(-1) (sqrt x) w.r.t. x

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  12. Find dy/dx, if x= cosec^2theta, y= cot^3theta, at theta = (pi)/6

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  13. Differentiate x^x w. r. t. x

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  14. Find dy/dx if y= sin^(-1)(3x-4x^3)

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  15. Find (d^2y)/(dx^2) if y= log(log x)

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  16. Using derivative prove that sin^(-1) x + cos^(-1)x = (pi)/2

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  17. Differentiate 7^x w.r.t. x^7

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  18. If y= A cos (log x) + B sin(log x), show that x^2 y2 + xy1 + y =0

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  19. Find the derivative of the inverse of function y= 2x^3 - 6x and calcul...

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  20. Differentiate tan^(-1) (frac{5-x}{6x^2 -5x -3}) w.r .t. x

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