Home
Class 12
MATHS
If f(x) is an even function, then wri...

If `f(x)` is an even function, then write whether `f^(prime)(x)` is even or odd.

Text Solution

AI Generated Solution

To determine whether \( f'(x) \) is even or odd given that \( f(x) \) is an even function, we can follow these steps: ### Step-by-Step Solution 1. **Definition of an Even Function**: Since \( f(x) \) is an even function, we have the property: \[ f(-x) = f(x) ...
Promotional Banner

Topper's Solved these Questions

  • DIFFERENTIALS, ERRORS AND APPROXIMATIONS

    RD SHARMA|Exercise Solved Examples And Exercises|102 Videos

  • DIRECTION COSINES AND DIRECTION RATIOS

    RD SHARMA|Exercise Solved Examples And Exercises|67 Videos

Similar Questions

Explore conceptually related problems

If f(x) is an odd function,then write whether f'(x) is even or odd.

If f(x) is an even function, then the curve y=f(x) is symmetric about

If f (x) is an even function, then the graph y = f (x) will be symmetrical about

If f(x) is an even function and f'(x) exist for all x then f'(1)+f'(-1) is

Whether function,f(x)=|x|-tan x is even or odd.

If f(x)=root(n)(x^(m)),n in N, is an even function, then m is even integer (b) odd integer any integer (d)f(x)- even is not possible

Let f(x)=|x-2|+|x-3|+|x-4| and g(x)=f(x+1). Then 1.g(x) is an even function 2.g(x) is an odd function 3.g(x) is neither even nor odd 4.g(x) is periodic

If f(t) is an odd function,then varphi(x)=int_(a)^(x)f(t)dt is an even function.

Let G(x)=(1/(a^x-1)+1/2)F(x), where a is a positive real number not equal to 1 and f(x) is an odd function. Which of the following statements is true? (a)G(x) is an odd function (b)G(x)i s an even function (c)G(x) is neither even nor odd function. (d)Whether G(x) is an odd or even function depends on the value of a

Statement 1: If f(x) is an odd function,then f'(x) is an even function.Statement 2: If f'(x) is an even function,then f(x) is an odd function.

RD SHARMA-DIFFERENTIATION-Solved Examples And Exercises
  1. If f(x)=log{(u(x))/(v(x))},\ u(1)=v(1) and u^(prime)(1)=v^(prime)(1)=2...

    Text Solution

    |

  2. If y=log(3x),\ \ x!=0 , find (dy)/(dx) .

    Text Solution

    |

  3. If f(x) is an even function, then write whether f^(prime)(x) is eve...

    Text Solution

    |

  4. If f(x) is an odd function, then write whether f^(prime)(x) is even...

    Text Solution

    |

  5. Write the derivative of sinx with respect to cosx .

    Text Solution

    |

  6. If f(x)=(log)(x^2)(logx) , then f^(prime)(x) at x=e is (a) 0 (b) 1 (c)...

    Text Solution

    |

  7. The differential coefficient of f(logx) with respect to x , where f(...

    Text Solution

    |

  8. The derivative of the function cot^(-1){(cos2x)^(1//2)} at x=pi//6 i...

    Text Solution

    |

  9. Differential coefficient of sec(tan^(-1)x) is (a)x/(1+x^2) (b) xsqrt...

    Text Solution

    |

  10. If y= tan^(-1)sqrt((1-sinx)/(1+sinx)), then the value of (dy)/(dx) at ...

    Text Solution

    |

  11. If y=(1+1/x)^x , then (dy)/(dx)= (a)(1+1/x)^x{log(1+1/x)-1/(x+1)} (b)...

    Text Solution

    |

  12. If x^y=e^(x-y) , then (dy)/(dx) is (a)(1+x)/(1+logx) (b) (1-logx)/(1+l...

    Text Solution

    |

  13. Given f(x)=4x^8 , then (a)f'(1/2)=f'(-1/2) (b) f(1/2)=-f'(-1/2) (c) f...

    Text Solution

    |

  14. If x=a\ cos^3theta,\ \ y=a\ sin^3theta , then (1+((dy)/(dx))^2)= (a)t...

    Text Solution

    |

  15. If y=sin^(-1)((1-x^2)/(1+x^2)) , then (dy)/(dx)= (a)-2/(1+x^2) (b) 2/...

    Text Solution

    |

  16. The derivative of sec^(-1)(1/(2x^2-1)) with respect to sqrt(1+3x) at x...

    Text Solution

    |

  17. For the curve sqrt(x)+sqrt(y)=1 , (dy)/(dx) at (1//4,\ 1//4) is (a)1//...

    Text Solution

    |

  18. If sin(x+y)=log(x+y) , then (dy)/(dx)= (a) 2 (b) -2 (c) 1 (d) -1]

    Text Solution

    |

  19. Let U=sin^(-1)((2x)/(1+x^2)) and V=tan^(-1)((2x)/(1-x^2)) , then (d U)...

    Text Solution

    |

  20. d/ dx { tan^ −1 ( cosx/ (1+sinx) ) } equals (a)1/2...

    Text Solution

    |