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If f(x)=((a+x)/(1+x))^(a+1+2x), show tha...

If `f(x)=((a+x)/(1+x))^(a+1+2x)`, show that ` f'(0) =a^(a+1)[2log a+(1-a^(2))/(a)]`.

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CHHAYA PUBLICATION-DIFFERENTIATION-EXERCISE 3A ( Long Answer Type Questions)
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  2. If cosy=x cos(a+y)," prove that " (dy)/(dx) =(cos^(2)(a+y))/(sin a), ...

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  3. If y^(x)=e^(y-x)" prove that, " (dy)/(dx)=((logey)^(2))/(log y).

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  4. If y= (x)/(2) sqrt(x^(2)-a^(2))-(a^(2))/(2) log (x+sqrt(x^(2)-a^(2)))...

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  5. If y= 2"sin"^(-1)(x-2)/(sqrt(6))-sqrt(2+4x-x^(2)), show that (dy)/(dx...

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  6. If f(x)=((a+x)/(1+x))^(a+1+2x), show that f'(0) =a^(a+1)[2log a+(1-a^...

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  7. If f(x)=((a+x)/(b+x))^(x)+cosx find f'(0).

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  8. If y=tan^(-1) [(sqrt(1+t^(2))+sqrt(1-t^(2)))/(sqrt(1+t^(2))-sqrt(1-t^...

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  9. If y="cot"^(-1) (sqrt(1+x)-sqrt(1-x))/(sqrt(1+x)+sqrt(1-x)), show tha...

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  10. If (1+x)^(n)=^(n)C(0)+^(n)C(1)x+^(n)C(2)x^(2)+…+^(n)C(n)x^(n), prove t...

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  11. If (1+x)^(n)=^(n)C(0)+^(n)C(1)x+^(n)C(2)x^(2)+…+^(n)C(n)x^(n), prove t...

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

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  13. If y=|(f(x),g(x),h(x)),(l,m,n),(a, b,c)|, prove that, (dy)/(dx)=|(f'(x...

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  14. If x^(2)+y^(2)=t+(1)/(t) and x^(4)+y^(4)=t^(2)+(1)/(t^(2)) then show t...

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  15. If y sqrt(x^(2)+1)=log(sqrt(x^(2)+1)-x), show that, (x^(2)+1)(dy)/(dx...

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  16. Using the method of differentiation deduce the formula of : cos(x+a...

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  17. Using the method of differentiation deduce the formula of : sin(x+a...

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  18. Using the method of differentiation deduce the formula of : sin2x s...

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  19. If y=1+(a(1)/(x-a(1))+(a(2)x)/((x-a(1))(x-a(2)))+(a(3)x^(2))/((x-a(1)...

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  20. If d/dx[(sinx)/sin(x-pi/4)] =kcosec^2(x-pi/4), find k and show that it...

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