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Let f(theta)=sin(tan^(-1)((sintheta)/(s...

Let `f(theta)=sin(tan^(-1)((sintheta)/(sqrt(cos2theta))))`, where `-pi/4ltthetaltpi /4`then the value of `d/ (d(tantheta)) f(theta)`is

A

1

B

2

C

3

D

4

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ARIHANT MATHS-DIFFERENTIATION -Exercise (More Than One Correct Option Type Questions)
  1. Let g(x) = log f(x), where f(x) is a twice differentiable positive fun...

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  2. If the functions f(x)=x^(3)+e^(x//2) " and " g(x)=f^(-1)(x), the value...

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  3. Let f(theta)=sin(tan^(-1)((sintheta)/(sqrt(cos2theta)))), where -pi/4...

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  4. If y=log(sinx)(tanx), then (dy)/ (dx) at x=(pi)/(4) is equal to

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  5. If y=sum(r=1)^(x) tan^(-1)((1)/(1+r+r^(2))), then (dy)/(dx) is equal t...

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  6. If f(x)=cot^(-1)((x^(x)-x^(-x))/(2)) then f'(1) equals

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  7. The function f(x)=e^x+x , being differentiable and one-to-one, has a d...

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  8. If f''(x)=-f(x) and g(x)=f^(prime)(x) and F(x)=(f(x/2))^2+(g(x/2))^2 a...

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  9. Write the subsets of {1,2}.

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  10. If x=f(t)cost-f^(prime)(t)sint and y=f(t)sint+f^(prime)(t)cost , then ...

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  11. If y=at^2+2bt-cand t = ax^2+2bx+c, then(d^3y)/(dx^3) equals

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  12. Differential coefficient of (x^((l+m)/(m-n)))^(1//(n-l))*(x^((m+n)/(n-...

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  13. if y=(A+Bx)e^(mx)+(m-1)^-1 e^x then (d^2y)/(dx^2)-2m(dy)/(dx)+m^2y is ...

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  14. If f(x)=-(x^(3))/(3)+x^(2)sina.sin2a-5sin^(-1)(a^(2)-8a+17),then

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  15. Let f and g be differentiable functions satisfying g(a) = b,g' (a) = ...

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  16. If f(x)=cos^(-1)1/(sqrt(13))(2cosx-3sinx) +sin^(-1)1/(sqrt(13))*(2cos...

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  17. If f(x)=sqrt(x+2sqrt(2x-4))+sqrt(x-2sqrt(2x-4)) then the value of 10 f...

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  18. Let y=1n(1+cosx)^2 . Then the value of (d^2y)/(dx^2)+2/(e^(y/2)) equal...

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  19. If f(x)=(a+sqrt(a^2-x^2)+x)/(sqrt(a^2-x^2)+a-x) where a>0 then f'(0) ...

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  20. Let u(x) and v(x) be differentiable functions such that (u(x))/(v(x))=...

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