Home
Class 12
MATHS
If x= e^t (sin t - cos t), y= e^t (sin t...

If `x= e^t (sin t - cos t)`, `y= e^t (sin t + cos t)`, find `dy/dx` at `t= pi/4`

Promotional Banner

Topper's Solved these Questions

  • Differentiation

    CHETANA PUBLICATION|Exercise Exercise|127 Videos

  • DIFFERENTIAL EQUATIONS

    CHETANA PUBLICATION|Exercise EXERCISE|254 Videos

  • Indefinite Integration

    CHETANA PUBLICATION|Exercise Exercise|221 Videos

Similar Questions

Explore conceptually related problems

If x=a ( tcos t- sin t ) ,y =a ( tsin t +cos t ),then (dy)/(dx) =

If x=e^t sin t , y=e^t cos t , t is a parameter , then (d^2y)/(dx^2) at (1,1) is equal to

If x= a(cos t + tsin t), y= a(sin t- t cos t) , then dy/dx .............. A) cot t B) -tan t C) sqrt (tan t) D) tan t

If x = ct and y=c/t , find (dy)/(dx) at t=2.

Find dy/dx if, x= 2cos t - cos2 t, y= 2sin t - sin 2t, at t= pi / 4

If x=sin tcos 2t , y=cos t sin 2t ,then " at " t= (pi)/(4) ,(dy)/(dx)=

If x= a sin t - b cos t, y= a cos t + b sin t , show that (d^2y)/(dx^2) = -(x^2 + y^2)/(y^3)

If x=a(cos t + log tan (t/2)) , y =a sin t then (dy)/(dx)=

Solve the following: If x = sin^(-1) (e^t), y= sqrt (1- e^(2t)) , show that sin x + dy/dx =0

CHETANA PUBLICATION-Differentiation-Exercise
  1. If x= sqrt (a^(sin^(-1) t)) and y= sqrt (a^(cos^(-1) t)), then show th...

    Text Solution

    |

  2. If x^2 + y^2 = t -(1/t) and x^4 + y^4 = t^2 + (1/ t^2), then show that...

    Text Solution

    |

  3. If x= e^t (sin t - cos t), y= e^t (sin t + cos t), find dy/dx at t= pi...

    Text Solution

    |

  4. Differentiate tan^(-1) (log t) w.r.t. log(sec^(-1) t)

    Text Solution

    |

  5. Differentiate log(sec x + tan x) w.r.t. x

    Text Solution

    |

  6. If y= log x, then find (d^2y) / (dx^2)

    Text Solution

    |

  7. If e^x + e^y = e^(x+y) , show that dy/dx = - e^(y-x)

    Text Solution

    |

  8. Find (d^2 y)/(dx^2) of the following: y= x^3 + 5x^2 -7x + 10

    Text Solution

    |

  9. Find (d^2 y)/(dx^2) of the following: y= log(frac{x^2}{e^x})

    Text Solution

    |

  10. Find (d^2 y)/(dx^2) of the following: y= sin(log x)

    Text Solution

    |

  11. Find (d^2 y)/(dx^2) of the following: y= x log x

    Text Solution

    |

  12. If ax^2 + 2hxy + by^2 =0, show that dy/dx = y/x

    Text Solution

    |

  13. Find (d^2 y)/(dx^2) of the following: x= sin sqrt t , y= sin sqrt t

    Text Solution

    |

  14. Find (d^2 y)/(dx^2) of the following: x = a cos^3theta, y= b sin^3thet...

    Text Solution

    |

  15. If x= costheta, y= sin^3theta, show that y(d^2 y)/(dx^2) + (dy/dx)^2 =...

    Text Solution

    |

  16. If y= cos (m sin^(-1) x), show that (1- x^2)(d^2 y)/(dx^2) - x(dy/dx) ...

    Text Solution

    |

  17. Find the nth derivative of the following: cos(5x+4)

    Text Solution

    |

  18. Find the nth derivative of the following: 1/x

    Text Solution

    |

  19. Find (d^2 y)/(dx^2) if y= x^2 + 3x +4

    Text Solution

    |

  20. Find the nth derivative of log x

    Text Solution

    |