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If x=asintheta " and " y=bcostheta, " th...

If `x=asintheta " and " y=bcostheta, " then " (d^(2)y)/(dx^(2))` is

A

`a/(b^(2))sec^(3)theta`

B

`-b/asec^(3)theta`

C

`-b/(a^(2))sec^(3)theta`

D

`-b^(2)/(a^(2))sec^(3)theta`

Text Solution

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The correct Answer is:
C
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PREMIERS PUBLISHERS-DIFFEREMTIAL CALCULUS DIFFERENTIABILITY AND METHODS OF DIFFERENTITAION -SOLUTION TO EXERCISE 10.5
  1. If y=cos(sinx^(2)), " then " (dy)/(dx) " at " x=sqrt(pi/2) is

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  2. If y=mx+c " and " f(0)=f'(0)=1, " then " f(2) is

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  3. If f(x)=xtan^(-1)x, then f'(1) is

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  4. d/dx(e^(x+5logx))

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  5. If the derivative of (ax-5)e^(3x) at x=0 is -13, then the value of a i...

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  6. x=(1-t^(2))/(1+t^(2)), y=(2t)/(1+t^(2)) " then " (dy)/(dx) is

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  7. If x=asintheta " and " y=bcostheta, " then " (d^(2)y)/(dx^(2)) is

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  8. The differential coefficient of log(10)x with respect to log(x)10 is

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  9. If f(x)=x+2, " then " f'(f(x)) at x=4 is

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  10. If y=(1-x)^(2)/x^(2), " then " (dy)/(dx)= is

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  11. If pv = 81, then (dp)/(dv) at v=9 is

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  12. If f(x) = {(x - 5, if xle1),(4x^(2) - 9, if (1ltxlt2),(3x +4, if xg...

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  13. It is given that f'(a) exists,then lim(xrarra)(xf(a) - af(x))/(x - a) ...

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  14. Assertion (A) : f(x)={{:(x+1",", x lt 2), (2x-1",", x ge 2):} then f'(...

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  15. If g(x) = (x^(2)+2x+3), f(x) and f(0)=5 and lim(xrarr0)(f(x)-5)/x = 4 ...

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  16. If f(x)={{:(x+2, -1 lt x lt 3), (5, x=3), (8-x, x gt 3):}, then at x=3...

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  17. The derivative of f(x)=xabs(x) at x=-3 is

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  18. If f(x)={{:(2a-x","" for "-altxlta),(3x-2a","" for "xgea):} then ...

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  19. If f(x)= {(ax^(2)-b, -1<x<1),(1/abs(x), elsewhere)} is differentia...

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  20. The number of points in R in which the function f(x) = abs(x - 1) + ab...

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