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If y=sqrt((1-x)/(1+x)) prove that (1-x^2...

If `y=sqrt((1-x)/(1+x))` prove that `(1-x^2)(dy)/(dx)+y=0`

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RD SHARMA ENGLISH-DIFFERENTIATION-All Questions
  1. Differentiate the following functions with respect to x : log(secx+ta...

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  2. Differentiate the following functions with respect to x : sec(logx^n)...

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  3. If y=sqrt((1-x)/(1+x)) prove that (1-x^2)(dy)/(dx)+y=0

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  4. If y=sqrt((1+e^x)/(1-e^x)),s howt h a t(dy)/(dx)=(e^x)/((1-e^x)sqrt(1...

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  5. Differentiate the following functions with respect to x : (log)(10...

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  6. If =(sqrt(a^2+x^2)+sqrt(a^2-x^2))/(sqrt(a^2+x^2)-sqrt(a^2-x^2)) , show...

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

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

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  9. Differentiate x^x with respect to xlogxdot

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

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

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  12. 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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  13. Differentiate logsinx with respect to sqrt(cosx) .

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

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

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

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  18. Differentiate the following functions with respect to x : (i)logsinx^...

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  19. Differentiate log sinx from first principle.

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  20. If f(x)=|logx|,xgt0,find f^(prime)(1/e)a n df^(prime)(e)

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