Home
Class 12
MATHS
If y=sinx+e^x ,t h e n(d^(2x))/(dy^2)= ...

If `y=sinx+e^x ,t h e n(d^(2x))/(dy^2)=` `(-sinx+e^x)^(-1)` `(sinx-e^x)/((cosx+e^x)^2)` (c) `(sinx-e^x)/((cosx+e^x)^3)` (d) `(sinx+e^x)/((cosx+e^x)^3)`

A

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

B

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

C

`(sin x - e^(x))/((cos x +e^(x))^(3))`

D

`(sin x + e^(x))/((cos x +e^(x))^(3))`

Text Solution

Verified by Experts

`y=sin x +e^(x)or (dy)/(dx)=cos x +e^(x)`
`"or "(dx)/(dy)=(cos x +e^(x))^(-1)" (1)"`
`therefore" "(d^(2)x)/(dy^(2))=-(cos x +e^(x))^(-2)(-sin x +e^(x))(dx)/(dy)`
Substituting the value of `(dy)/(dx)` from (1),
`(d^(2)x)/(dy^(2))=((sin x -e^(x)))/((cos x +e^(x))^(2))(cos x +e^(x))^(-1)=(sin x-e^(x))/((cos x +e^(x))^(3))`
Promotional Banner

Topper's Solved these Questions

  • DIFFERENTIATION

    CENGAGE|Exercise Exercise (Multiple)|22 Videos

  • DIFFERENTIATION

    CENGAGE|Exercise Exercise (Comprehension)|23 Videos

  • DIFFERENTIATION

    CENGAGE|Exercise Exercise 3.9|14 Videos

  • DIFFERENTIAL EQUATIONS

    CENGAGE|Exercise Question Bank|25 Videos

  • DOT PRODUCT

    CENGAGE|Exercise DPP 2.1|15 Videos

Similar Questions

Explore conceptually related problems

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

If y=sinx+e^(x), Then find (dy)/(dx) .

If y=e^(-x)cosx, show that (d^(2)y)/(dx^(2))=2e^(-x)sinx.

(e^(x))/(sinx)

y = sinx.e^x . Find dy/dx

e^(sinx)sin(e^(x))

int e^sinx cosx dx

If y=x+e^(x), then (d^(2)x)/(dy^(2)) is (a) e^(x)(b)-(e^(x))/((1+e^(x))^(3))(c)-(e^(x))/((1+e^(x))^(3))(d)(-1)/((1+e^(x))^(3))

I=int(e^(x)+e^(-x)+(e^(x)-e^(-x))sin x)/(1-cosx)

e^(x)((cosx-sinx)/(sin^(2)x))

CENGAGE-DIFFERENTIATION-Exercise (Single)
  1. Let f(x) be a polynomial of degree 3 such that f(3)=1,f^(prime)(3)=-1,...

    Text Solution

    |

  2. If y^2=a x^2+b x+c , then y^3(d^2y)/(dx^2) is (a) a constant (b) a fun...

    Text Solution

    |

  3. If y=sinx+e^x ,t h e n(d^(2x))/(dy^2)= (-sinx+e^x)^(-1) (sinx-e^x)/(...

    Text Solution

    |

  4. If y= sin px and y(n) is the n^(th) derivative of y, then |{:(y,y(1)...

    Text Solution

    |

  5. If f^(x)=-f(x)a n dg(x)=f^(prime)(x)a n d F(x)=(f(x/2))^2+(g(x/2))^2 ...

    Text Solution

    |

  6. Let y=1n(1+cosx)^2 . Then the value of (d^2y)/(dx^2)+2/(e^(y/2)) equal...

    Text Solution

    |

  7. x=tcost ,y=t+sintdot Then (d^(2x))/(dy^2)a tt=pi/2 is (pi+4)/2 (b) -(p...

    Text Solution

    |

  8. "If "f(x)=(x-1)^(4)(x-2)^(3)(x-3)^(2)(x-4), then the value of f'''(1)+...

    Text Solution

    |

  9. let y=t^(10)+1, and x=t^8+1, then (d^2y)/(dx^2) is

    Text Solution

    |

  10. If x = log p and y=(1)/(p), then

    Text Solution

    |

  11. If x=varphi(t), y=psi(t),t h e n(d^(2y))/(dx^2) is (varphi^(prime)psi^...

    Text Solution

    |

  12. If f(x)=x^4tan(x^3)-x1n(1+x^2), then the value of (d^4(f(x)))/(dx^4) ...

    Text Solution

    |

  13. If graph of y=f(x) is symmetrical about the y-axis and that of y=g(x) ...

    Text Solution

    |

  14. Let g(x) be the inverse of an invertible function f(x), which is diffe...

    Text Solution

    |

  15. f(x)=e^(x)-e^(-x)-2 sin x -(2)/(3)x^(3). Then the least value of n for...

    Text Solution

    |

  16. Let y=f(x) and x=(1)/(z)." If "(d^(2)y)/(dx^(2))=lamda(z^(3))(dy)/(dz)...

    Text Solution

    |

  17. Let x=f(t) and y=g(t), where x and y are twice differentiable function...

    Text Solution

    |

  18. If f(x) satisfies the relation f((5x-3y)/2)=(5f(x)-3f(y))/2AAx ,y in ...

    Text Solution

    |

  19. A function f: RvecR satisfies xcosy(f(2x+2y)-f(2x-2y)=cosxsiny(f(2x+2y...

    Text Solution

    |

  20. If y=asinx+bcosx , then y^2+((dy)/(dx))^2 is a

    Text Solution

    |