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Find the derivative of f given by f(x)=s...

Find the derivative of f given by `f(x)=sin^(-1)x`assuming it exists.

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Given that
`f(x)=sin^ (−1) x`
`⇒f ...
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NCERT-CONTINUITY AND DIFFERENTIABILITY-SOLVED EXAMPLES
  1. Find (dy)/(dx)if x-y =pi

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  2. Find (dy)/(dx), if y + siny = cosx

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  3. Find the derivative of f given by f(x)=sin^(-1)xassuming it exists.

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  4. Find the derivative of / given by f(x)=tan^(-1)xassuming it exists.

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  5. Find df/dx if f(x) = (sin x) ^ sin x for all o lt x lt pi .

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  6. Differentiate sin^2xw.r.t e^(cosx).

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  7. Differentiate the following w.r.t x.(i) sqrt(3x+2)+(1/(sqrt(2x^2 + 4))...

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  8. Find fprime(x)if f(x)=(sinx)^(sinx)for all 0ltxltpi

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  9. Verify Rolles theorem for the function y=x^2+2,a=-2and b = 2.

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  10. Verify the Mean Value Theorm for f(x)=x^2 in the interval [2,4].

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  11. If y=3e^(2x)+2e^(3x). Prove that (d^2y)/(dx^2)-5(dy)/(dx)+6y=0.

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  12. If y=sin^(-1)x, show that (1-x^2)(d^2y)/(dx^2)-x(dy)/(dx)=0.

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  13. Find all the points of discontinuity of the function f defined byf(x)=...

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  14. Discuss the continuity of the function f defined by f(x)={(x+2,"if",x...

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  15. Discuss the continuity of the function f given by f(x)={x , ifxgeq0x^2...

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  16. Discuss the continuity of the function defined byf(x)={x+2, ifx<0-x+2,...

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  17. Find all the points of discontinuity of the greatest integer function...

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  18. Show that every polynomial function is continuous.

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  19. Discuss the continuity of sine function.

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  20. Prove that every rational function is continuous.

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