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if y = x^(x^2), show that dy/dx = x^(x^(...

`if y = x^(x^2), show that dy/dx = x^(x^(2))x(1+2logx) `

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x^(2)(dy)/(dx) = x^(2) - 2y^(2) + xy

(i)If y = x^(3) + x^(2) + x +1 then dy/dx at x = 1 is 0 (ii)If y=sin^(-1)((2x)/(1+x^(2))) then dy/dx = tanx (iii) y = x^(x) dy/dx = x^(x)[1+logx] (iv) y = tan^(-1)x, dy/dx = 1/(1 + x^(2) state which pair of the statement given above are true.

PREMIERS PUBLISHERS-DIFFEREMTIAL CALCULUS DIFFERENTIABILITY AND METHODS OF DIFFERENTITAION -PROBLEMS FOR PRACTICE
  1. y = log sec(pi/4 + x/2), show that dy/dx=1/2tan(pi/4+x/2)

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  2. If y = cos^(-1)((1-x)/(1+x)), show that dy/dx =1/(sqrt(x)(1+x))

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  3. if y = x^(x^2), show that dy/dx = x^(x^(2))x(1+2logx)

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  4. If y = x^(a)+a^(x)+x^(x)+a^(a), dind dy/dx.

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  5. find dy/dx if y = (logx)^(sin^(-1)x

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  6. f(x) = x^(x)+ x^(1/x), find f'(x).

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  7. y = tan^(-1)((3x-x^(3))/(1-3x^(2))), find dy/dx.

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

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  9. Find the derivatives of the following : tan^(-1)((cosx+sinx)/(cosx-s...

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  10. If y = tan^(-1)((1+x^(2))/(1-x^(2))) Find dy/dx.

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  11. y = tan^(-1)((sqrt(x)+sqrt(a))/(1-sqrt(ax))), find dy/dx.

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  12. y = tan^(-1)((sqrt(1+x)-sqrt(1-x))/(sqrt(1+x)+sqrt(1-x))),find dy/dx.

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  13. y = cot^(-1)((sqrt(1+sinx)+sqrt(1-sinx))/(sqrt(1+sinx)-sqrt(1-sinx))),...

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  14. Differentiate cosec^(-1)(1/(3x-4x^(3))):

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  15. If x=asec^(3)theta " and " y=atan^(3)theta " find " (dy)/(dx) " at " t...

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  16. If x = 2costheta- cos 2theta, y = 2sintheta -sin 2theta, find dy/dx.

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  17. x = a(costheta + logtan(theta/2), y = asintheta, find dy/dx.

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  18. If x^(m)y^(n) = (x+y)^(m+n),find dy/dx.

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  19. If e^(x)+ e^(y) = e^(x+y), find dy/dx.

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  20. If ax^(2) +2hxy + by^(2) + 2gx + 2fy + c = 0, find dy/dx.

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