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Differentiate the following w.r.tx: lo...

Differentiate the following w.r.tx:
`log(sinsqrt(1+x^2))`

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MODERN PUBLICATION-CONTINUITY AND DIFFERENTIABILITY-EXERCISE
  1. Differentiate the following w.r.t. x: x^2e^x sinx

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  2. Differentiate the following w.r.tx: e^(sec^2 x) + 3 cos^-1x

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  3. Differentiate the following w.r.tx: log(sinsqrt(1+x^2))

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  4. Differentiate the following w.r.t. x: sin(logx), x>0

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  5. Differentiate the following w.r.tx: log(cos5x)

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  6. Differentiate the following w.r.tx: cot(logx+e^(sqrtx))

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  7. Differentiate the following w.r.tx: 2ln((x-1)/(x+1))

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  8. Differentiate the following w.r.tx: x^2ln((sqrt((x^2+9)/(x^2+4))))

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  9. Differentiate the following w.r.tx: ln(Sec x + tanx)

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  10. Differentiate the following w.r.tx: log((1+x)/(1-x))

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  11. Differentiate the following w.r.t.x. log tan (pi/4 + x/2)

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  12. Differentiate the following w.r.t.x. sin^(-1)(2xsqrt(1 - x^2))

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  13. Find dy/dx if y=x^x

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  14. Find dy/dx when: xy + ce^-y + ye^x = x^2

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  15. If 1/2 (e^y - e^-y) = x, prove that : dy/dx = 1/(sqrt(1+x^2))

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  16. If xy = e^(x - y), prove that (dy)/(dx) = (y (x - 1))/(x (y + 1))

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  17. If y = (sin^-1x)/(sqrt(1-x^2)), prove that (1-x^2)(dy/dx)- xy = 1

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  18. If x=tan((1)/(2)logy), then show that (1+x^(2))(d^(2)y)/(dx^(2))=(a-2x...

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  19. Differentiate tan^-1((2^(x+1))/(1-4^x)) with respect to x.

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  20. If y = log10 sin x, prove that dy/dx=(log10 e) cotx

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