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If the derivative of tan^(-1)(a+b x) tak...

If the derivative of `tan^(-1)(a+b x)` takes the value 1 at `x=0` , prove that `1+a^2=b` .

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RD SHARMA ENGLISH-DIFFERENTIATION-All Questions
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  2. If y=cos^(-1)(2x)+2cos^(-1)sqrt(1-4x^2),\ \ \ x \ \ is \ [0,1/2] , fi...

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

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  5. 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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  6. If y=cos^(-1){(2x-3sqrt(1-x^2))/(sqrt(13))},"f i n d"(dy)/(dx)

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  7. Differentiate the following with respect to x : sin^(-1)((2^(x+1). 3^x...

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  9. If x^2+2x y+y^3=42 , find (dy)/(dx)

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  10. If x^3+y^3=3a x y , find (dy)/(dx)

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  11. If log (x^2+y^2)=2t a n^(-1)\ (y/x), then show that (dy)/(dx)=(x+y)/(x...

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  12. Find dy/dx if x=sqrt(1+y)

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  13. If cos^(-1)((x^2-y^2)/(x^2+y^2))=tan^(-1)a , prove that (dy)/(dx)=y/xd...

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  14. If siny=xsin(a+y), prove that (dy)/(dx)= (sin^2(a+y))/(sina) .

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  15. If sqrt(1-x^6)+sqrt(1-y^6)=a(x^3-y^3),prove that (dy)/(dx)=(x^2)/(y^2...

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  16. If x^2+y^2=t-1/t and x^4+y^4=t^2+1/(t^2) , then prove that (dy)/(dx)=1...

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  18. If y=cos^(-1)sqrt((cos3x)/(cos^3x)),then show (dy)/(dx)=sqrt(3/(cosx...

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  19. If x y=c^2 , find (dy)/(dx)

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  20. If y^3-3x y^2=x^3+3x^2\ y , find (dy)/(dx)

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