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If y = f(x^(2) + 2) " and " f'(3) = 5 , ...

If `y = f(x^(2) + 2) " and " f'(3) = 5 , " then" dy/dx " at x " = 1` is

A

15

B

5

C

10

D

25

Text Solution

Verified by Experts

The correct Answer is:
C
We have , ` y = f(x^
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MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS-DIFFERENTIATION -EXERCISE 2 (MISCELLANEOUS PROBLEMS)
  1. If 5f(x)+3f(1/x)=x+2 and y=x f(x), then find dy/dx at x=1.

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  2. If y is a function of x and log(x+y)-2xy=0 then the value of y (0) is ...

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  3. If y = f(x^(2) + 2) " and " f'(3) = 5 , " then" dy/dx " at x " = 1 is

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  4. If y = log ((1-x^(2))/(1+x^(2))), then (dy)/(dx) is equal to

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  5. let f(x)=e^x ,g(x)=sin^(- 1) x and h(x)=f(g(x)) then find (h^(prime)(x...

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  6. If y = (cos x)^((cosx)^((cos x)...oo)), " then " dy/dx is equal to

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  7. If cos(x/2) cos (x/2^2) cos (x/2^) ..... cos (x/2^n)=sinx/(sin(x/2^n) ...

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  8. If x = log (1 + t^(2)) " and " y = t - tan^(-1)t, " then" dy/dx is e...

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  9. If the function y(x) reprsented by x = sin t , y = ae^(tsqrt(2)) + be...

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  10. If y=sqrt((a-x)(x-b))-(a-b)tan^(-1)(sqrt(a-x)/sqrt(x-b)) then dy/dx=

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  11. If x=sectheta-costheta,y=sec^(10)theta-cos^(10)theta and (x^(2)+4)((dy...

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

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  13. If x^(y) = e^(2(x-y)), " then" f'(x) is equal to

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  14. If sqrt(1-x^(2n))+sqrt(1-y^(2n))=a^n(x^n-y^n), prove that y^(n-1)*sqr...

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  15. If f(x)=sin^(-1)(sinx)+cos^(-1)(sinx) and phi(x)=f(f(f(x))), then phi'...

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  16. Let x^cosy + y^cosx = 5, then

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  17. If y = sin x^(@) " and " u = cos x " then " (dy)/(dx) is equal to

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  18. If y=tan^(-1)1/(1+x+x^2)+tan^(-1)1/(x^2+3x+3)+tan^(-1)1/(x^2+5x+7)++ u...

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  19. If y=tan^(-1)((sinx+cosx)/(cosx-sinx)) , then (dy)/(dx) is equal to

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  20. If y = cos^(-1) ((2cos x - 3 sin x)/(sqrt(13))), " then" (dy)/(dx) i...

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