Home
Class 12
MATHS
If y=secx+tanx then prove that (d^2y)/(d...

If `y=secx+tanx` then prove that `(d^2y)/(dx^(2))=cosx/((1-sinx)^(2))`.

Text Solution

AI Generated Solution

To prove that \(\frac{d^2y}{dx^2} = \frac{\cos x}{(1 - \sin x)^2}\) given \(y = \sec x + \tan x\), we will follow these steps: ### Step 1: Rewrite \(y\) Start with the given function: \[ y = \sec x + \tan x \] Using the definitions of secant and tangent, we can rewrite \(y\) as: ...
Promotional Banner

Topper's Solved these Questions

  • Continuity and Differentiability

    NAGEEN PRAKASHAN ENGLISH|Exercise Exercies 5a|30 Videos
  • Continuity and Differentiability

    NAGEEN PRAKASHAN ENGLISH|Exercise Exercies 5b|8 Videos
  • APPLICATIONS OF INTEGRALS

    NAGEEN PRAKASHAN ENGLISH|Exercise Miscellaneous Exercise|19 Videos
  • DETERMINANTS

    NAGEEN PRAKASHAN ENGLISH|Exercise Miscellaneous Exercise|19 Videos

Similar Questions

Explore conceptually related problems

If y=tanx+secx , prove that (d^2y)/(dx^2)=(cosx)/((1-sinx)^2)

If y=tanx+secx ,p rov e \ t h a t \ (d^2y)/(dx^2)=(cosx)/((1-sinx)^2)

If y=e^tanx then prove that: cos^2x(d^2y)/(dx^2)-(1+sin2x)(dy)/dx=0

Solve: (d^2y)/dx^2=cosx-sinx

If y=2sinx+3cosx , show that (d^2y)/(dx^2)+y=0 .

If y=log(sinx) , prove that (d^3y)/(dx^3)=2cosx cos e c^3x .

If y=tanx , prove that y_2=2y y_1 .

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

If y=e^x(sin x+cosx) prove that (d^2y)/(dx^2)-2 (dy)/(dx)+2y=0 .

If y=e^x(sinx+cosx) prove that (d^2y)/(dx^2)-2(dy)/(dx)+2y=0 .

NAGEEN PRAKASHAN ENGLISH-Continuity and Differentiability-Miscellaneous Exercise
  1. If y=secx+tanx then prove that (d^2y)/(dx^(2))=cosx/((1-sinx)^(2)).

    Text Solution

    |

  2. Differentiate w.r.t. x the function. (3x^2-9x+5)^9

    Text Solution

    |

  3. Differentiate w.r.t. x the functionsin^3x+cos^6x

    Text Solution

    |

  4. y=(5x)^(3cos 2x) then find (dy)/(dx).

    Text Solution

    |

  5. sin^(-1)(xsqrt(x)),0 le x le 1

    Text Solution

    |

  6. Differentiate w.r.t. x the function (cos^(-1)x/2)/(sqrt(2x+7)),-2<x<2

    Text Solution

    |

  7. Prove that:cot^(-1)((sqrt(1+sinx)+sqrt(1-sinx))/(sqrt(1+sinx)-sqrt(1-s...

    Text Solution

    |

  8. (log x)^(log x),x gt1

    Text Solution

    |

  9. Differentiate w.r.t. x the function cos" "(a" "cos" "x" "+" "b" "s in"...

    Text Solution

    |

  10. If y=(sinx-cosx)^(sinx-cosx),pi/4<x<(3pi)/4,"f i n d"(dy)/(dx)dot

    Text Solution

    |

  11. Differentiate w.r.t. x the function x^x+x^a+a^x+a^a ,for some fixed a...

    Text Solution

    |

  12. Differentiate x^x^(2-3)+(x-3)^x^2 with respect to x :

    Text Solution

    |

  13. Find (dy)/(dx),if y=12(1-cost), x=10(t-sint)

    Text Solution

    |

  14. If y=sin^(-1)x+sin^(-1)sqrt(1-x^2) , find (dy)/(dx) in each of the ...

    Text Solution

    |

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

    Text Solution

    |

  16. "If "(x-a)^(2)+(y-b)^(2)=c^(2), for some cgt0, prove that ([1+((dy)/(d...

    Text Solution

    |

  17. "If "cos y = x cos(a+y)," with "cos a ne pm1," prove that "(dy)/(dx)=(...

    Text Solution

    |

  18. If x=a(cost+tsint) and y=a(sint-tcost), find (d^2y)/(dx^2)

    Text Solution

    |

  19. If f(x)=|x|^3 , show that f"(x) exists for all real x and find it.

    Text Solution

    |

  20. Using mathematical induction prove that d/(dx)(x^n)=n x^(n-1) for all...

    Text Solution

    |

  21. Using the fact that s in (A + B) = s in A cos B + cos A s in Band the ...

    Text Solution

    |