Home
Class 11
MATHS
If f(x)a n dg(x) are two differentiable ...

If `f(x)a n dg(x)` are two differentiable functions, show that `f(x)g(x)` is also differentiable such that `d/(dx)[f(x)g(x)]=f(x)d/(dx){g(x)}+g(x)d/(dx){f(x)}`

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • COMPLEX NUMBERS

    RD SHARMA|Exercise Solved Examples And Exercises|267 Videos
  • ELLIPSE

    RD SHARMA|Exercise Solved Examples And Exercises|97 Videos

Similar Questions

Explore conceptually related problems

If f(x) and g(x) a re differentiate functions, then show that f(x)+-g(x) are also differentiable such that (d)/(dx){f(x)+-g(x)}=(d)/(dx){f(x)}+-(d)/(dx){g(x)}

If f(x) and g(x) are differentiable function then show that f(x)+-g(x) are also differentiable such that d(f(x)+-g(x))/(dx)=d(f(x))/(dx)+-d(g(x))/(dx)

If f(x) and g(f) are two differentiable functions and g(x)!=0, then show trht (f(x))/(g(x)) is also differentiable (d)/(dx){(f(x))/(g(x))}=(g(x)(d)/(pi){f(x)}-g(x)(d)/(x){g(x)})/([g(x)]^(2))

Let f(x) be a differentiable and let c a be a constant.Then cf(x) is also differentiable such that (d)/(dx){cf(x)}=c(d)/(dx)(f(x))

Theorem : (i)Differentiation of a constant function is 0 (ii) Let f(x) be the differentiable function and let c be a constant.Then cf(x) is also differentiable such that d(cf(x))/(dx)=cd((f(x))/(dx)

If x=f(t) and yy=g(t) are differentiable functions of t then (d^(2)y)/(dx^(2)) is

Using the first principle,prove that: (d)/(dx)(f(x)g(x))=f(x)(d)/(dx)(g(x))+g(x)(d)/(dx)(f(x))

If y =f(u) is differentiable function of u, and u=g(x) is a differentiable function of x, then prove that y= f [g(x)] is a differentiable function of x and (dy)/(dx)=(dy)/(du)xx(du)/(dx) .

int[(d)/(dx)f(x)]dx=

If (d)/(dx)[f(x)]=f(x), then intf(x)[g'(x)+g''(x)]dx=

RD SHARMA-DERIVATIVES-Solved Examples And Exercises
  1. If f(x)=alphax^n , prove that alpha=(f^(prime)(1))/n .

    Text Solution

    |

  2. Differentiate the following functions with respect to x :(a x+b)^n(c...

    Text Solution

    |

  3. If f(x)a n dg(x) are two differentiable functions, show that f(x)g(x) ...

    Text Solution

    |

  4. The differentiation of (log)a x (a >0) with respect to x i.e. d/(dx)(...

    Text Solution

    |

  5. If y=sqrt(x/a)+sqrt(a/x) , prove that 2x y(dy)/(dx)=(x/a-a/x)

    Text Solution

    |

  6. If for f(x)=lamdax^2+mux+12 and f'(4)=15 and f'(2)=11, then find lamda...

    Text Solution

    |

  7. Differentiate x^2cosx

    Text Solution

    |

  8. Using first principles, prove that d/(dx){1/(f(x))}=-(f^(prime)(x))/({...

    Text Solution

    |

  9. If y=sqrt((1-cos2x)/(1+cos2x),)x in (0,pi/2)uu(pi/2,pi), then find (dy...

    Text Solution

    |

  10. The differentiation of loge x ,i s1/xdot i.e. d/(dx)((loge x)=1/x)

    Text Solution

    |

  11. Differentiate the following functions with respect to x from first...

    Text Solution

    |

  12. Differentiate x^n by first princeple

    Text Solution

    |

  13. Differentiate the following functions with respect to x from first p...

    Text Solution

    |

  14. The differentiation of t a nx with respect to x is sec^2xdot i.e. d/(...

    Text Solution

    |

  15. The differentiation of cotx with respect to x is-cos e c^2xdot i.e. ...

    Text Solution

    |

  16. (x) The differentiation of secx with respect to x is secxtanx

    Text Solution

    |

  17. The differentiation of cos e cx with respect to xis -c o s e cxcotxdot...

    Text Solution

    |

  18. The differentiation of e^-x with respect to x is -e^-xdot i.e. d/(dx)...

    Text Solution

    |

  19. Differentiate the following functions with respect to x : e^(3logx...

    Text Solution

    |

  20. Let f(x) be a differentiable and let c a be a constant. Then cf(x) is ...

    Text Solution

    |