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It g(x) is the inverse of f(x) and f(X) = `(1+x^3)^-1`, show that g'(x) = `1/(1 + {g(x)}^3)`.

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UNITED BOOK HOUSE-MISCELLANEOUS EXERCISE-EXERCISE
  1. Evaluate the following limits: underset(x rarr0)lim(sinx + cos x)^(1/x...

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  2. Evaluate the following limits: underset(x rarr0)limsinlog(1+x)/log(sin...

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  3. It g(x) is the inverse of f(x) and f(X) = (1+x^3)^-1, show that g'(x) ...

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  4. Find the differential coefficients of the folloiwng functions: x^x

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  5. Find form 1st principle the differential coefficients of the folloiwng...

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  6. Find form 1st principle the differential coefficients of the folloiwng...

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  7. Find dy/dx when x^(siny) + y ^(sinx) = 1

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  8. Find dy/dx when x^(logx) + (sinx)^x + 15 x

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  9. Find (d^2y)/(dx^2) when x= e^-t and y = te^-1

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  10. Find (d^2y)/(dx^2) when x= a sin^3t and y = a cos^3 t at t = pi/4

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  11. Find (d^2y)/(dx^2) when x=a(t-sint) and y = a (1+cost) at t = pi/...

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  12. If y^2 (1-x^2) = x^2 +1, show that (1-x^4) (dy/dx)^2 = y^4 -1.

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  13. If x = sec theta - cos theta, y = sec^n theta - cos^n theta, then show...

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  14. If y= x^(y^x), prove that y1 = (ylogy(1+x logx logy)/(x log x (1-xlogy...

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  15. or,find the derivatives of tan^(-1) ((sqrt(1+x^2)-1)/x) with respect t...

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  16. If y = (Sin ^-1 x)^2 + (cos^-1 x)^2, then show that (1-x^2) y 2 - xy1 ...

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  17. If y=x log[x// (a+bx)], show that x^3y2 - (y-xy1)^2 = 0

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  18. If x^3 + y^3 = 3ax^2, show that y2 + (2a^2x^2)/(y^5) = 0

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  19. Evaluate: int(x^2+1)/(x^4+x^2+1) dx

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  20. Evaluate: intdx/(sin^4x + cos^4x)

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