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If f^(1)(x)=sin(logx)andy=f((2x+3)/(3-2x...

If `f^(1)(x)=sin(logx)andy=f((2x+3)/(3-2x))` then `(dy)/(dx)` is

A

`sin(logx).(1)/(xlogx)`

B

`12/((3-2x)^2)sin[log((2x+3)/(3-2x))]`

C

`sin[log((2x+3)/(3-2x))]`

D

`sin(logx)`

Text Solution

Verified by Experts

The correct Answer is:
B
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AAKASH SERIES-DIFFRENTATION-PRACTICE SHEET (EXERCISE - I) (LEVEL - I)(Straight Objective Type Questios)
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  2. If f(x) = |cos x - sin x| , then f^(1)(pi/4) =

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  3. If f^(1)(x)=sin(logx)andy=f((2x+3)/(3-2x)) then (dy)/(dx) is

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  4. The value of 3 f(x ) - 2 f(1/x)=x then f^(1)(2) =

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  5. If u = f(x^2) , v = g(x^3), f^(1)(x) = sinx , g^(1)(x) = cos x then fi...

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  6. If sqrt(u/v)+sqrt(v/u)=6 , then (du)/(dv) =

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  7. If x = theta -(1)/(theta) , y = theta + (1)/(theta) then (dy)/(dx) =

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  8. sqrt((y)/( x))+ sqrt((x)/(y))= 2 implies (dy)/(dx) =

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  9. If f(x) = (ax + b) Cos x +(cx +d) Sin x and f^(1) (x) = x Cosx is an a...

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  10. If f(1) = 3 ,f'(1)=-1/3 , then the derivative of {x^(11) +f(x)}^(-2) a...

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  11. Let f(x+y)=f(x)f(y) and f(x) = 1 + (sin2x) g(x) where g(x) is continu...

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  12. If y = f((3x+4)/(5x+6)) and f^(1)(x) = tanx^2 then (dy)/(dx) is equal...

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  13. If y =a sin x + b cos x , then y^2 + ((dy)/(dx))^2 is a

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  14. Let h(x) be differentiable for all x and let f(x) = (kx+e^(x)),h(x) wh...

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  15. d/(dx){Tan^(-1)((asinx + b cosx)/(acosx-bsinx))} =

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  16. d/(dx)[tanh^(-1)((2x)/(1+x^2))]=

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  17. If g is the inverse of f and f'(x) = 1/(2+x^n) , then g^(1)(x) is equa...

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  18. The derivative of sin^(-1)((2x)/(1+x^2)) with respect to cos^(-1)((1-x...

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  19. If y = Sin ^(-1) (1 - x ^(2))/(1+ x ^(2)) then (dy)/(dX)=

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  20. If y = cos^(-1)((a^(2)-x^(2))/(a^(2)+x^(2)))+sin^(-1)((2ax)/(a^(2)+x^(...

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