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If x = a(cos(Theta) + (Theta)sin(Theta))...

`If x = a(cos(Theta) + (Theta)sin(Theta)) y= a(sin(Theta) -(Theta)cos(Theta)) show that a(Theta)(d^(2)y)/(dx^(2)) = sec^(3)(Theta)`.

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The correct Answer is:
`a(Theta) = sec^(3)(Theta)`
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PREMIERS PUBLISHERS-DIFFEREMTIAL CALCULUS DIFFERENTIABILITY AND METHODS OF DIFFERENTITAION -PROBLEMS FOR PRACTICE
  1. If x = a(cos(Theta) + (Theta)sin(Theta)) y= a(sin(Theta) -(Theta)cos(...

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  2. If y = 1/root(3)(x)+log(5)x+8, find dy/dx.

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  3. Differentiate log(e)x from first principles.

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  4. y = a sinx log(10)x + e^(2x), find dy/dx.

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  5. y = log sec(pi/4 + x/2), show that dy/dx=1/2tan(pi/4+x/2)

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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