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Let f(x) be a polynomial in x . Then the...

Let `f(x)` be a polynomial in `x` . Then the second derivative of `f(e^x)wdotrdottdotxi s` `f^(e^x)dote^x+f^(prime)(e^x)` `f^(e^x)dote^(2x)+f^(prime)(e^x)dote^(2x)` `f^(e^x)e^(2x)` (d) `f^(e^x)dote^(2x)+f^(prime)(e^x)dote^x`

A

`f(e^(x)).e^(x)+f(e^(x))`

B

`f(e^(x)).e^(2x)+f(e^(x)).e^(2x)`

C

`f'(e^(x))e^(2x)`

D

`f'(e^(x)).e^(2x)+f(e^(x)).e^(x)`

Text Solution

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The correct Answer is:
D
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MOTION-METHOD OF DIFFERENTIATION-EXERCISE - 1
  1. If y=(1+x)(1+x^2)(1+x^4)(1+x^(2n)), then find (dy)/(dx)a tx=0.

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  2. If y=sin^(-1)((x^2-1)/(x^2+1))+sec^(-1)((x^2+1)/(x^2-1)) then dy/dx is...

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  3. Find the derivative of sec^(-1)((1)/(2x^(2)-1))" w.r.t. "sqrt(1-x^(2))...

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  4. If y = sin^-1((2x)/(1+x^2)) then (dy)/(dx) at x=-2is

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  5. If y=x-x^2, then the derivative of y^2 w.r.t x^2 is

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  6. The differential cofficient of a^(sin^(-1)x)w.r.t sin^(-1)x is -

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  7. The value of derivative of tan^(-1)((2xsqrt(1-x^(2)))/(1-2x^(2)))w.r...

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  8. If x=e^(y+e^(y^(+..."to"00))),xgt0,"then"(dy)/(dx)

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  9. If y=sqrt(x)^(sqrt(x)^(sqrt(x)^sqrt(x)...00)), "then the value of"(dy)...

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  10. If y=sqrt(logx+sqrt(logx+sqrtlogx+......oo)), " then " dy/dx is

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  11. If y=cos^(-1)(cosx),t h e n(dy)/(dx) is equal to x/y (b) y/(x^2) (x^2...

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  12. If 8f(x)+6f(1/x)=x+5 and y=x^2(f(x), then (dy)/(dx) at x=-1 is equal t...

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  13. If f(x)=x^(n),"n" epsilon N, then the value of f(1)-(f^(')(1))/(1!)+(f...

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  14. LEt f(x) be a differentiable function and f'(4)=5. Then, lim(x->2)(f(4...

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  15. If u=a x+b ,t h e n(d^n)/(dx^n)(f(a x+b)) is equal to (d^n)/(d u^n)(f(...

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  16. Let f(x) be a polynomial in x . Then the second derivative of f(e^x)wd...

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  17. If f(x), g(x), h(x) are polynomials in x of degree 2 If F(x)=|[f,g,h],...

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  18. If y=f(x) is an odd differentiable function defined on (-oo,oo) such t...

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  19. If x=(1+t)/(t^3),y=3/(2t^2)+2/t ,t h e nx((dy)/(dx))^3-(dy)/(dx) is eq...

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  20. If x=a t^2,y=2a t , then (d^2y)/(dx^2) is equal to -1/(t^2) (b) 1/(2a...

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