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Differentiate tan^(-1)((1+2x)/(1-2x))w i...

Differentiate `tan^(-1)((1+2x)/(1-2x))w i t hr e s p e c ttosqrt(1+4x^2)`

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RD SHARMA-DIFFERENTIATION-Solved Examples And Exercises
  1. If y=sqrt{a^{2}-x^{2}}, prove that y frac{d y}{d x}+x=0

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  2. Differentiate tan^(-1)((sqrt(1+x^2)-1)/x) with respect to tan^(-1)x ,x...

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  3. Differentiate tan^(-1)((1+2x)/(1-2x))w i t hr e s p e c ttosqrt(1+4x^2...

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  4. Differentiate x^x with respect to xlogxdot

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  5. Differentiate sin^(-1)((2x)/(1+2x)) wrt to tan^(-1)x , -1<x<1.

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  6. If x=sectheta-costheta and y=sec^n theta- cos^n theta then show that (...

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  7. If u=sin(mcos^(-1)x),v=cos(msin^(-1)x),p rov et h a t(d u)/(d v)=sqrt(...

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  8. Differentiate logsinx with respect tosqrt(cosx) .

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  9. Find (dy)/(dx),w h e n x=e^(theta)(theta+1/theta)a n dy=e^(-theta)(th...

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  10. If f(x)=|x+a^2a b a c a b x+b^2b c a bb c x+c^2|,fin df^(prime)(x)dot

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  11. Differentiate tan^(-1){(sqrt(1+x^2)-sqrt(1-x^2))/(sqrt(1+x^2)+sqrt(1-x...

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  12. Differentiate the following functions with respect to x : (x^2+x+1)^...

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  13. Differentiate the following functions with respect to x : (i)logsin...

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  14. Differentiate log sinx from first principle.

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  15. If f(x)=|logx|,xgt0,find f^(prime)(1/e) and f^(prime)(e)

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  16. Differentiate sin^(-1)sqrt(x)(0ltxlt1) from first principles.

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  17. Differentiate sin^(-1)(2x+3) from first principles.

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  18. Differentiate the following functions with respect to x : (2^2cotx)/(...

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  19. If f(x)=|cosx-sinx|,find f^(prime)(pi/6)a n df^(prime)(pi/3)dot

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

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