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If u, v, w are three differentiable func...

If `u, v, w` are three differentiable functions of `x`,
prove that `d/dx (uvw) = ((du)/dx)vw + u ((dv)/dx) w + uv ((dw)/dx)`. Use this result to differentiate `x^(3)(x^(2)+1)(x^(4)+1)` w.r.t. x.

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V PUBLICATION-LIMITS AND DERIVATIVES-QUESTION BANK
  1. Find the derivative of (x + cos x) (x- tan x)

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  2. Differentiate (4x+5sin x)/(3x+7 cos x)

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  3. Find the derivative of f(x)=(x^(2)cos (pi/4))/(sin x)

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  4. Find the derivative of [x/(1+tan x)]

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  5. Differentiate (x+sec x)(x-tan x)

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  6. Evaluatelim(x rarr 1) (2/(1-x^(2))+1/(x-1))

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  7. Evaluate: lim(x rarr 0) x/(sqrt(a+x)-sqrt(a-x))

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  8. Find the value of k, if lim(x rarr 1) (x^(4)-1)/(x-1) = lim(x rarr k)(...

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  9. Evaluate lim(x rarr 1) ((x + x^2 + .........+ x^n)-n)/(x - 1)

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  10. Evaluate the following limits lim(x rarr 0) (tan x - sin x)/x^(3)

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  11. Evaluate: lim(x rarr 0) (sin 2x + sin 6x)/(sin 5x - sin 3x)

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  12. Evaluate: (i) lim(x rarr 1) (x^(2)+6x+4) (ii)lim(x rarr 4) (x^(3)+4)/(...

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  13. Evaluate lim(x rarr 1) (sqrt(x^(2)-1)+sqrt(x-1))/(sqrt(x^(2)-1))

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  14. Find k so that lim(x rarr 2) f(x) exists, where f(x) = {(2x+3 if xle2)...

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  15. If for the function h, given by h(x) = kx^(2)+7x-4, h^(')(5)=97, find ...

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  16. If u, v, w are three differentiable functions of x, prove that d/dx ...

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  17. If y = 1 + x/(1!)+x^(2)/(2!)+x^(3)/(3!)+...., show that dy/dx = y.

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  18. It is known that for x ne 1, we have 1+x+x^(2)+….+x^(n-1)= (1-x^(n))/(...

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  19. Evalute lim(xrarr1)(x^7-1)/(x^4-1)

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  20. If xy=c^2 , prove that x^2dy/dx+c^2=0

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