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Find (dy)/(dx), if y=(cosx)^(x)+(sinx)^(...

Find `(dy)/(dx)`, if `y=(cosx)^(x)+(sinx)^(1//x)`.

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Verified by Experts

The correct Answer is:
`(cosx)^(x)[-x tanx+logcosx]+(sinx)^(1//x)`
`[(cotx)/(x)-(log(sinx))/(x^(2))]`
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ARIHANT PUBLICATION-CONTINUITY AND DIFFERENTIABILITY -CHAPTER PRACTICE (4 MARK)
  1. If y=x^(sinx-cosx)+(x^(2)-1)/(x^(2)+1), then find (dy)/(dx)

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  2. If y=(sinx)^(x)+sin^(-1)sqrt(x), then find (dy)/(dx).

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  3. Find (dy)/(dx), if y=(cosx)^(x)+(sinx)^(1//x).

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  4. If x=alphasin2t(1+cos2t) and y=betacos 2t(1-cos2t), then show that (dy...

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  5. Find the derivative of the function w.r.t. x at x=1, cos^(-1)[sinsqrt(...

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  6. If y=e^(m sin ^(-1)x), then show that (1-x^(2))(d^(2)y)/(dx^(2))-x(dy)...

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  7. Test the continuity and differentiability at x=1 of the function f def...

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  8. Show that the function f(x)=|x-1|+|x-2| is not differentiable at x=2.

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  9. If a function f is differentiable at a point c, then prove that it is ...

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  10. If x=acos^(3)theta,y=a sin^(3)theta,then find (d^2y)/dx^(2)

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  11. Find the derivative of (x+sinx)/(x+cosx) w.r.t. x.

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  12. Differentiate w.r.t. x, sin^(-1)[(2^(x+1)*3^(x))/(1+(36)^(x))].

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  13. If y=(sin(ax+b))/(cos(cx+d)), the find (dy)/(dx).

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  14. Differentiate tan^(-1)((x)/(sqrt(1-x^(2)))) w.r.t. sin^(-1)(2xsqrt(1-x...

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  15. If y=tan^(-1)((a)/(x))+logsqrt((x-a)/(x+a)), then prove that (dy)/(dx)...

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  16. If x=a((1-t^(2))/(1+t^(2))) and y=(2t)/(1-t^(2)), then find (dy)/(dx).

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  17. If x=a(costheta+log"tan"(theta)/(2)) and y=asin theta, then find the v...

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  18. Differentiate x^(xcosx)+(x^(2)+1)/(x^(2)-1) w.r.t. x.

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  19. If y=(sin x - cos x)^((sinx-cosx)),(pi)/(4)ltxlt(3pi)/(4), then find (...

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  20. If log(sqrt(1+x^(2))-x)=ysqrt(1+x^(2)), then show that (1+x^(2))(dy)/(...

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