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If x=log t, y=sin t, find dy/dx at t=pi/...

If `x=log t`, `y=sin t`, find `dy/dx` at `t=pi/2`. State true or false in exercises `14-21`.

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USHA PUBLICATION-CONTINUITY AND DIFFERENTIABILITY APPLICATION OF DERIVATIVES -EXERCISE
  1. If y=sin^-1x and z=2cos^-1x, find dy/dz.

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  2. If y=t^2 and x=t^3 find, dy/dx at t=1.

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  3. If x=log t, y=sin t, find dy/dx at t=pi/2. State true or false in exer...

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  4. Differential coefficient of sin^-1((2x^3)/(1+x^6)) with respect to x i...

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  5. There is no function which is its own derivative

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  6. The derivative of a non constant even function is always an odd functi...

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  7. If x=cos^-1(1/(sqrt(1+t^2))), y=sin^-1(1/(sqrt(t^2+1))) then dy/dx is ...

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  8. The derivative of sec^-1(1/(2x^2-1)) w.r.t. sqrt(1-x^2) is 3

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  9. Derivative of log10sinx w.r.to x is cotx.log10e

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  10. If y=sec^(-1)(sqrtx+1)/sqrtx+sin^(-1)fracsqrtx(sqrtx+1)then dy/dx=

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  11. f(x)=xabsx is derivable at x=0.

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  12. Fill in the blanks : The derivative of sec^-1x w.r.to x if xlt-1 is

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  13. Fill in the blanks : The derivative of sec^-1x w.r.to x if xgt1 is

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  14. Fill in the blanks : The derivative of cosec^-1x w.r.to x if xgt1 is

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  15. Fill in the blanks : The derivative of cosec^-1x w.r.to x if xlt-1 is

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  16. Fill in the blanks : The derivative of sin^-1x w.r.to x if -1ltxlt1 is

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  17. Fill in the blanks : The derivative of cos^-1x w.r. to x if -1ltxlt1 i...

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  18. Fill in the blanks : The derivative of abs(2x-5) when xlt5/2 is

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  19. Give an example of a function which is neither one-one nor onto

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  20. Check the injectivity of the following function f: R rarr R is given b...

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