Home
Class 12
MATHS
"If "y= sin x +e^(x)," then "(d^(2)x)/(d...

`"If "y= sin x +e^(x)," then "(d^(2)x)/(dy^(2))=`

A

`(-sinx+e^(x))^(-1)`

B

`(sinx-e^(x))/((cos+e^(x))^(2))`

C

`(sinx-e^(x))/((cosx+e^(x))^(3))`

D

`(sinx+e^(x))/((cosx+e^(x))^(3))`

Text Solution

Verified by Experts

The correct Answer is:
C
We have,
`y=sinx+e^(x)`
`implies" "(dy)/(dx)=cosx+e^(x)`
`implies" "(dx)/(dy)=(cosx+e^(x))^(-1)`
`implies" "(d^(2)x)/(dy^(2))=-(cosx+e^(x))^(-2)(-sinx+e^(x))(dx)/(dy)`
`(d^(2)x)/(dy^(2))=(sinx-e^(x))/((cosx+e^(x))^(2)).(cosx+e^(x))^(-1)=(sinx-e^(x))/((cosx+e^(x))^(3))`
Promotional Banner

Topper's Solved these Questions

  • DIFFERENTIATION

    OBJECTIVE RD SHARMA ENGLISH|Exercise Section I - Solved Mcqs|92 Videos

  • DIFFERENTIATION

    OBJECTIVE RD SHARMA ENGLISH|Exercise Exercise|58 Videos

  • DIFFERENTIALS, ERRORS AND APPROXIMATIONS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Exercise|17 Videos

  • ELLIPSE

    OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test|29 Videos

Similar Questions

Explore conceptually related problems

y=sinx+e^(x) then (d^(2)x)/(dy^(2)) is:

If y=x+e ^(x), then ((d^(2)y)/(dy ^(2)))_(x = ln 2) is :

If y= sin (8 sin ^(-1) x ) then (1-x ^(2)) (d^(2)y)/(dx ^(2))-x (dy)/(dx)=- ky, where k =

If y=sin(log_(e)x) , then x^(2)(d^(2)y)/(dx^(2))+x(dy)/(dx) is equal to

If y=x+e^x , find (d^2x)/(dy^2) .

y=e^(x)"sin"5x then find (d^2y)/(dx^(2)) .

If y=sin (sinx) prove that (d^(2)y)/(dx^(2)) + "tan x" (dy)/(dx) + y cos^(2) x =0 .

If y=e^(x)sin x , then find (dy)/(dx)

If y =sin (sin x) and (d^(2)y)/(dx^(2))+(dy)/(dx) tan x + f(x) = 0, then find f(x).

If y sin (sin x) and (d^(2)y)/(dx^(2))+(dy)/(dx) tan x + f(x) = 0, then find f(x).

OBJECTIVE RD SHARMA ENGLISH-DIFFERENTIATION-Chapter Test
  1. "If "y= sin x +e^(x)," then "(d^(2)x)/(dy^(2))=

    Text Solution

    |

  2. If f(x)=log(e)[log(e)x], then what is f' (e) equal to?

    Text Solution

    |

  3. If e^y+xy=e then the value of (d^2y)/(dx^2) for x=0 is

    Text Solution

    |

  4. If sqrt(x+y) +sqrt(y-x)=5, then (d^(2)y)/(dx ^(2))=

    Text Solution

    |

  5. "If "ax^(2)+2hxy+by^(2)=1," then "(d^(2)y)/(dx^(2)) is

    Text Solution

    |

  6. If f(x)=sin{(pi)/(2)[x]-x^(5)},1ltxlt2 and [.] denotes the greatest in...

    Text Solution

    |

  7. f(x) is a polynomial of degree

    Text Solution

    |

  8. If y=sin(log(e)x), then x^(2)(d^(2)y)/(dx^(2))+x(dy)/(dx) is equal to

    Text Solution

    |

  9. If f(x)=(1-x)^n, then the value of f(0)+f^(prime)(0)+(f^('')(0))/(2!)+...

    Text Solution

    |

  10. "If "xsqrt(1+y)+ysqrt(1+x)=0," prove that "(dy)/(dx)=-(1)/((x+1)^(2)).

    Text Solution

    |

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

    Text Solution

    |

  12. If y=sin^(-1){(5x+12 sqrt(1-x^(2)))/(13)}, find (dy)/(dx).

    Text Solution

    |

  13. If f(x)=cos^(-1){(1-(log(e)x)^(2))/(1+(log(e)x)^(2))}, then f'( e )

    Text Solution

    |

  14. y=sin^(-1)[sqrt(x-ax)-sqrt(a-ax)]

    Text Solution

    |

  15. Let f(x)=(x^3+2)^(30) If f^n (x) is a polynomial of degree 20 where f^...

    Text Solution

    |

  16. If f(x)=cos^(2)x+cos^(2)(x+(pi)/(3))+sinxsin(x+(pi)/(3)) and g((5)/(4)...

    Text Solution

    |

  17. If f(x)=10cosx+(13+2x)sinx then f''(x)+f(x)=

    Text Solution

    |

  18. Let a function f:RtoR satisfy the equation f(x+y)=f(x)=f(Y)AAx, yepsil...

    Text Solution

    |

  19. If f(x)=log{(u(x))/(v(x))},\ u(1)=v(1) and u^(prime)(1)=v^(prime)(1)=2...

    Text Solution

    |

  20. If f'(x)=arc tan((x^(x)-x^(-x))/(2)), then f'(1) is equal to

    Text Solution

    |

  21. Let f(x)=2^(2x-1)" and "g(x)=-2^(x)+2xlog2. Then the set of points sat...

    Text Solution

    |