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Differentiate tan^(-1)(x/(sqrt(1-x^...

Differentiate `tan^(-1)(x/(sqrt(1-x^2)))` with respect to `sin^(-1)(2xsqrt(1-x^2)),` if `-1/(sqrt(2)) < x< 1 /(sqrt(2))`

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RD SHARMA ENGLISH-DIFFERENTIATION-All Questions
  1. If y={log(cosx)sinx}"{"log(sinx)cosx")"^(-1)+sin^(-1)((2x)/(1+x^2)), ...

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  2. If y=sec^(-1)((x+1)/(x-1))+sin^(-1)((x-1)/(x+1)),x > 0. Find (dy)/(dx)...

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  3. Differentiate tan^(-1)(x/(sqrt(1-x^2))) with respect to sin^(...

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  4. Differentiate sin^(-1)sqrt(1-x^2) with respect to cot^(-1)(x/sqrt(1...

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  5. If ysqrt(x^2+1)=log(sqrt(x^2+)1-x),s howt h a t(x^2+1)(dy)/(dx)+x y+1=...

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  6. If e^x+e^y=e^(x+y) , prove that (dy)/(dx)=-(e^x(e^y-1))/(e^y(e^x-1)) o...

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  7. If y=xsin(a+y),p rov et h a t(dy)/(dx)=(sin^2(a+y))/(sin(a+y)-ycos(a+y...

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  8. If x ylog(x+y)=1,p rov e \ t h a t \ (dy)/(dx)=-(y(x^2y+x+y))/(x(x y^2...

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  9. If y=(sinx-cosx)^(sinx-cosx) ,pi/4 ltxlt (3pi)/ 4 find dy/dx

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  10. If y=log((x^2+x+1)/(x^2-x+1))+2/(sqrt(3))t a n^(-1)((sqrt(3)x)/(1-x^2)...

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  11. If (x-y)e^(x/(x-y))=a , prove that (dy)/(dx)+x=2ydot

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  12. Differentiate the following functions with respect to x : (e^xlogx)/...

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  13. Differentiate the following functions with respect to x: log(x+sqrt...

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  14. Differentiate the following functions with respect to x : tan(e^(s...

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  15. Differentiate sin^(-1){(2^(x+1). 3^x)/(1+(36)^x)}"w i t hr e s p e...

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  16. Differentiate the following functions with respect to x: log((sinx)...

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  17. If y=tan^(-1){(sqrt(1+x)-sqrt(1-x))/(sqrt(1+x)+sqrt(1-x))},"f i n d"(d...

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  18. Differentiate the following function sqrt((1+sinx)/(1-sinx))

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  19. If the derivative of tan^(-1)(a+b x) take the value of 1 at x=0,...

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  20. Differentiate the following functions with respect to x: e^(3x)cos2...

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