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If y=sin^(-1)(x/(sqrt(1+x^2)))+cos^(-1)(...

If y=`sin^(-1)(x/(sqrt(1+x^2)))`+`cos^(-1)(1/(sqrt(1+x^2)))` , prove that `(dy)/(dx)=(2x)/(1+x^2)` .

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RD SHARMA ENGLISH-DIFFERENTIATION-All Questions
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  2. If y=sin^(-1)((2x)/(1+x^2))+sec^(-1)((1+x^2)/(1-x^2)) , prove that (dy...

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  6. If y=cot^(-1)[(sqrt(1+sinx)+sqrt(1-sinx))/(sqrt(1+sinx)-sqrt(1-sinx))]...

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  7. If y=tan^(-1)((2x)/(1-x^2))+sec^(-1)((1+x^2)/(1-x^2)) , x >0 , prove t...

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

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  9. If y=sin[2tan^(-1){sqrt((1-x)/(1+x))}],find(dy)/(dx)

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

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

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  16. If a x^2+2\ h x y+b y^2+2\ gx+2\ fy+c=0 , find (dy)/(dx) .

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

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

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

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

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