Home
Class 11
MATHS
If y=f(x^3),z=g(x^5),f^(prime)(x)=tanx ,...

If `y=f(x^3),z=g(x^5),f^(prime)(x)=tanx ,a n dg^(prime)(x)=secx ,` then find the value of `lim_(x->0)(((dy)/(dz)))/x`

Promotional Banner

Topper's Solved these Questions

  • DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS

    CENGAGE PUBLICATION|Exercise Multiple correct answers type|11 Videos
  • LINEAR INEQUALITIES

    CENGAGE PUBLICATION|Exercise All Questions|68 Videos

Similar Questions

Explore conceptually related problems

If u=f(x^3),v=g(x^2),f^(prime)(x)=cosx ,a n dg^(prime)(x)=sinx ,t h e n(d u)/(d v) is

If f(a)=2,f^(prime)(a)=1,g(a)=-1,g^(prime)(a)=2, then the value of lim_(x->a)(g(x)f(a)-g(a)f(x))/(x-a) is (a) -5 (b) 1/5 (c) 5 (d) none of these

Let g: RvecR be a differentiable function satisfying g(x)=g(y)g(x-y)AAx , y in R and g^(prime)(0)=aa n dg^(prime)(3)=bdot Then find the value of g^(prime)(-3)dot

If lim_(xtoa)[f(x)+g(x)]=2 and lim_(xtoa) [f(x)-g(x)]=1, then find the value of lim_(xtoa) f(x)g(x).

Iff(x)=e^(g(x))a n dg(x)=int_2^x(tdt)/(1+t^4), then find the value of f^(prime)(2)

If f((x+2y)/3)=(f(x)+2f(y))/3AAx ,y in Ra n df^(prime)(0)=1,f(0)=2, then find f(x)dot

If y=(a+b x^(3/2))/(x^(5/4))a n dy^(prime)=0a tx=5, then the value of (a^2)/(b^2) is_______

If f(x)=xtan^(-1)x , find f^(prime)(sqrt(5)) .

If f(x)=xtan^(-1)x , find f^(prime)(sqrt(3)) .

If f(a) = 2, f'(a) = 1, g(a) = -1 and g'(a) = 2 , find the value of lim_(x rarr a)(g(x)f(a) - g(a)f(x))/(x-a)

CENGAGE PUBLICATION-LIMITS AND DERIVATIVES-All Questions
  1. Find the derivative of sec^(-1)(1/(2x^2-1)) w.r.t sqrt(1-x^2) at x=1/...

    Text Solution

    |

  2. If y=(1/2)^(n-1)cos(ncos^(-1)x), then prove that y satisfies the diffe...

    Text Solution

    |

  3. If y=f(x^3),z=g(x^5),f^(prime)(x)=tanx ,a n dg^(prime)(x)=secx , then ...

    Text Solution

    |

  4. If x in (0,pi/2), then show that cos^(-1)(7/2(1+cos2x)+sqrt((sin^2x-48...

    Text Solution

    |

  5. "If "f(x)=|{:(x+a^(2),ab,ac),(ab, x+b^(2),bc),(ac,bc, x+c^(2)):}|," th...

    Text Solution

    |

  6. If y=cos^(-1)((2x)/(1+x^2)),t h e n(dy)/(dx)i s (a)(-2)/(1+x^2) fo...

    Text Solution

    |

  7. If f(x),g(x) and h(x) are three polynomials of degree 2, then prove th...

    Text Solution

    |

  8. If f(x-y), f(x) f(y) and f(x+y) are in A.P. for all x , y ,and f(0)!=0...

    Text Solution

    |

  9. If x^3+y^3+3a x y=0 , f i n d dy / dx

    Text Solution

    |

  10. If 1 is the twice repeated root of the equation a x^3+b x^2+b x+d=0,t ...

    Text Solution

    |

  11. If log(x^2+y^2)=2tan^(-1)(y/x), show that (dy)/(dx)=(x+y)/(x-y)

    Text Solution

    |

  12. If y=btan^(-1)(x/a+tan^(-1)y/x),find(dy)/(dx)dot

    Text Solution

    |

  13. Let y=sqrt(x+sqrt(x+sqrt(x+oo))) , (dy)/(dx) is equal to (a)1/(2y-...

    Text Solution

    |

  14. If y=sqrt(sinx+y), then find (dy)/(dx)

    Text Solution

    |

  15. f(x)=|x^2-3|x|+2|dot Then which of the following is/are true f^(prime)...

    Text Solution

    |

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

    Text Solution

    |

  17. If x^3-2x^2y^2+5x+y-5=0 and y(1)=1, then (a)y^(prime)(1)=4/3 (b) y...

    Text Solution

    |

  18. If x^y=e^(x-y), Prove that dy/dx=logx/(1+logx)^2

    Text Solution

    |

  19. Let f(x)=(sqrt(x-2sqrt(x-1)))/(sqrt(x-1)-1)xdot Then (a)f^(prime)(10...

    Text Solution

    |

  20. If sqrt(x) +sqrt(y)=4, f i n d (dx/dy) a t (y = 1).

    Text Solution

    |