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If (cosx)^(y)=(siny)^(x), then find (dy)...

If `(cosx)^(y)=(siny)^(x),` then find `(dy)/(dx)`.

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Verified by Experts

The correct Answer is:
`(log(siny)+ytanx)/(log(cosx)-xcoty)`
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ACCURATE PUBLICATION-DIFFERENTIABILITY-QUESTIONS CARRYING 4 MARKS
  1. Find dy/dx when : y = x^(cotx) +(2x^2-3)/(x^2+x+2)

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

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  3. If (cosx)^(y)=(siny)^(x), then find (dy)/(dx).

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  4. If y=x^(cotx)+(sinx)^(x), find (dy)/(dx).

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  5. Differentiate (sinx)^(x)+(cosx)^(sinx) w.r.t. x.

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  6. Differentiate sin^-1(2^(x+1)/(1+4^x)) w.r.t x

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  7. Differentiate the following with respect to x: sin^-1[(2^(x+1).3^x)/...

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  8. If y=cos^(-1)((2^(x+1))/(1+4^(x))), find (dy)/(dx).

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  9. If y = sin^(-1) ((2x)/(1 + x^2)) + sec^(-1) ((1 + x^2)/(1 - x^2)) , pr...

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  10. If y = tan^(-1)((sqrt(1 + x^2) - sqrt(1 - x^2))/(sqrt(1 + x^2) + sqrt(...

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  11. If y = sin^-1[xsqrt(1-x) - sqrtx (sqrt(1-x^2))] find dy/dx

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

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  13. Differentiate tan^(-1)((sqrt(1 - x^2))/(x)) w.r.t. cos^(-1)(2x sqrt(1 ...

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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. Find the derivative of sec^(-1)((1)/(2x^(2)-1))" w.r.t. "sqrt(1-x^(2))...

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  16. Find (dy)/(dx) when y=(sinx)^(x)+sin^(-1)sqrt(x).

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  17. If y = 3 cos (log x) + 4 sin (log x) show that x^2 y2 + xy1 + y = 0

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  18. If y=e^(ax)cosbx, then prove that (d^(2)y)/(dx^(2))-2a(dy)/(dx)+(a^(2)...

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  19. If (a+bx)e^(y//x)=x, show that x^(3)y''=(xy'-y)^(2).

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  20. If y=x^(3)log((1)/(x)), prove that (d^(2)y)/(dx^(2))-(2)/(x)(dy)/(dx)+...

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