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Differentiate the following w.r.t x. (i)...

Differentiate the following w.r.t x. (i) `cos^(-1)(sinx)` (ii) `tan^(-1)((sinx)/(1+cosx))` (iii) `sin^(-1)((2^(x+1))/(1+4^x))`

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The correct Answer is:
`3/(2sqrt(3x+2))-(2x)/((2x^(2)+4)^(3/2))`
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MODERN PUBLICATION-CONTINUITY AND DIFFERENTIABILITY-EXERCISE 5(c) (SHORT ANSWER TYPE QUESTIONS)
  1. Differentiate the following w.r.t.x : sin(x^2)

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  2. Differentiate the following w.r.t.x : sin^(4)(ax+b)^(2)

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  3. Differentiate the following w.r.t.x : sin(cotx)

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  4. Differentiate the following w.r.t.x : cosec(cotsqrtx)

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  5. Differentiate the following w.r.t.x : sin^(2)(x^(5))

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  6. Differentiate the following w.r.t.x : cos^(2)(x^(3))

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  7. Differentiate the following w.r.t.x : cosx^(3).sin^(2)(x^(5))

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  8. Differentiate the following w.r.t.x : 2sqrt(cot(x^(2)))

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  9. Differentiate the following w.r.t x. (i) cos^(-1)(sinx) (ii) tan^(...

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  10. Differentiate the following w.r.t.x : sqrt(15x^(2)-x+1)

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  11. Differentiate the following w.r.t.x : (sin(ax+b))/(cos(cx+d))

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  12. Differentiate w.r.t. x the function cos" "(a" "cos" "x" "+" "b" "s in"...

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  13. Find dy/dx if : y=9u^(2),u=1-3/2x^(2)

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  14. Find dy/dx if : y=(3-v)/(2+v),v=(4x)/(1-x^(2))

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  15. Find dy/dx if : y=at^(2),t=x/(2a)

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  16. Find (dy)/(dx) at x=1,y=pi/4 if sin^2 y+cos xy0

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  17. If x^(16)y^(9)=(x^(2)+y)^(17), prove that dy/dx=(2y)/x.

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  18. Differentiate the following w.r.t. x: |2x - 1|

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  19. Differentiate the following w.r.t. x: |2x^(2)-3|

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  20. If y+siny=cosx, then find the values of 'y' for which dy/dx is valid.

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