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Given that d/(dx) (c1u1 +- c2u2 +- ........

Given that `d/(dx) (c_1u_1 +- c_2u_2 +- .........+- c_nu_n) = c_1d/(dx)(u_1) +- c_2d/(dx)(u_2) +- ....... +- c_nd/(dx)(u_n)` and `d/(dx) (c) = 0` if `c,c_1,c_2,...........,c_n` are constants and `u_1, u_2,.....,u_n` are functions of x.
After expanding the square, differentiate `(sqrtx + 1/sqrtx)^2` w.r.t. x

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Given that d/(dx) (c_1u_1 +- c_2u_2 +- .........+- c_nu_n) = c_1d/(dx)(u_1) +- c_2d/(dx)(u_2) +- ....... +- c_nd/(dx)(u_n) and d/(dx) (c) = 0 if c,c_1,c_2,...........,c_n are constants and u_1, u_2,.....,u_n are functions of x. Using the given results, evaluate d/(dx) ((3x^2 + 12x - 11)/x)

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Verify that the function y=c_1 e^(a x) cos b x+c_2 e^(a x) sin b x , where c_1, c_2 are arbitrary constants is a solution of the differential equation. ((d^2 y)/(d x^2))-2 a (dy)/(dx)+(a^2+b^2) y=0

Choose the correct . The general solution of the differential equation (y dx - x dy)/y =0 is a) xy =c b) x= cy^2 c)y = cx d)y= cx^2

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A N EXCEL PUBLICATION-LIMITS AND DERIVATIVES-QUESTION BANK
  1. Consider the function f(x) = { ((x^2 - 4)/abs(x-2) : x ne 2), (2 : x =...

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  2. Given that d/(dx) (c1u1 +- c2u2 +- .........+- cnun) = c1d/(dx)(u1) +-...

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  3. Given that d/(dx) (c1u1 +- c2u2 +- .........+- cnun) = c1d/(dx)(u1) +-...

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  4. Fill in the blanks d/(dx) (2x + 3) = ..................

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  5. Fill in the blanks d/(dx) (5x^2 - 7x +1)=..............

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  6. Using product rule differentiate (2x + 3)(5x^2 - 7x + 1) w.r.t. x

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  7. Expand (2x + 3)(5x^2 - 7x +1) as a single polynomial and differentiate...

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  8. Sajan finds the derivate of two functions f(x) =x^2 + cos x and g(x) =...

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  9. Fill in the blanks d/(dx) (cos x) =....

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  10. d/dx(tan x)=………

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  11. Express (8 cos^2 x + 11 sin x)/(cos x) as the sum of function and henc...

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  12. If sin (x + y) =1/2 , prove that y = sin^-1 (1/2) - x

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  13. Prove that (dy)/(dx)= -1

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  14. What are the values of d/(dx) (cos x) and d/(dx) ( tan x)

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  15. Using the product rule and the relation tan x cos x = sin x , find d/(...

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  16. Writing cos x = (sin x)/(tan x) and apply quotient rule find d/(dx) (c...

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  17. Differentiate 1-2 tan x w.r.t.x

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  18. Differentiate 5 + 4 sin x w.r.t.x

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  19. Using product rule differentiate (1-2tan x) ( 5 + 4 sin x) w.r.t.x

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  20. Find d/(dx) ( 1 + tan x)

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