Home
Class 11
MATHS
Using the first principle, prove that d/...

Using the first principle, prove that `d/(dx)(1-x^2)=-2x`

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

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

prove that d/dx(x^x)=x^x(1+log_ex)

Using the formula of differentiation of product functions show that (d)/(dx)(x^(n))=nx^(n-1) , where n is a positive integer.

Differentiate the function with respect to x using the first principle : cos^2x

Using the formula (d)/(dx)(tan^(-1)x)=(1)/(1+x^(2)) , deduce that (d)/(dx)(cot^(-1)x)=-(1)/(1+x^(2)) .

State whether the following statement is true or false : (d)/(dx)(cos^(-1)x-sin^(-1)x)=(2)/(sqrt(1-x^(2))) , when |x|lt1 .

Differentiate (from 1st principle) sinx/xwith respect to x

If f (x) = tan ^(-1) ((cos x- sinx)/(cos x+ sin x)) then the value of (d)/(dx) f(x) is-

Which of the following is the value of (d)/(dx){|x-1|+|x-5|} at the point x = 3 ?

If u and v are two differentiable functions of x show that, (d)/(dx)("tan"^(-1)(u)/(v))=(v (du)/(dx)-u(dv)/(dx))/(u^(2)+v^(2)) .

CENGAGE PUBLICATION-LIMITS AND DERIVATIVES-All Questions
  1. Evaluate lim(h->0)((a+h)^2sin^(-1)(a+h)-a^2sin^(-1)a)/h

    Text Solution

    |

  2. If x^2+y^2=1, then (a)y y^('')-2(y^(prime))^2+1=0 (b)yy^('')+(y...

    Text Solution

    |

  3. Using the first principle, prove that d/(dx)(1-x^2)=-2x

    Text Solution

    |

  4. If y is function of x and log(x+y)=2xy, then find the value of y'(0).

    Text Solution

    |

  5. Find the derivative of sqrt(4-x) w.r.t. x using the first principle.

    Text Solution

    |

  6. The slope of the tangent to the curve (y-x^5)^2=x(1+x^2)^2 at the poin...

    Text Solution

    |

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

    Text Solution

    |

  8. Let f(theta)=sin(tan^(-1)((sintheta)/(sqrt(cos2theta)))), where -pi/4...

    Text Solution

    |

  9. Find the derivative of e^(sqrt(x)) w.r.t. x using the first principle.

    Text Solution

    |

  10. f(x)=tan^(-1){log(e/x^2)/log(ex^2)}+tan^(-1)((3+2logx)/(1-6logx)) then...

    Text Solution

    |

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

    Text Solution

    |

  12. If f(x)=|x^2-5x+6|,t h e nf^(prime)(x)e q u a l s 2x-5for2<x<3 5-2xf...

    Text Solution

    |

  13. If graph of y=f(x) is symmetrical about the point (5,0) and f^(prime)(...

    Text Solution

    |

  14. Let f(x^m y^n)=mf(x)+nf(y) for all x , y in R^+ and for all m ,n in ...

    Text Solution

    |

  15. Let g: RvecR be a differentiable function satisfying g(x)=g(y)g(x-y)AA...

    Text Solution

    |

  16. If f,g,a n d \ h are differentiable functions of x and d(x)=|[f,g,h]...

    Text Solution

    |

  17. Let f be a function such that f(x+y)=f(x)+f(y) for all x and y and f(...

    Text Solution

    |

  18. If f((x+y)/3)=(2+f(x)+f(y))/3 for all x,y f'(2)=2 then find f(x)

    Text Solution

    |

  19. Prove that lim(x->0) (f(x+h)+f(x-h)-2f(x))/h^2 = f''(x)

    Text Solution

    |

  20. Let f(x+y)=f(x)+f(y)+2x y-1 for all real x and y and f(x) be a differe...

    Text Solution

    |