Home
Class 12
MATHS
Differentiate a^xw.r.t. x, where a is a...

Differentiate `a^x`w.r.t. x, where a is a positive constant.

Text Solution

AI Generated Solution

To differentiate \( a^x \) with respect to \( x \), where \( a \) is a positive constant, we can follow these steps: ### Step 1: Define the function Let \( y = a^x \). ### Step 2: Take the natural logarithm of both sides Taking the natural logarithm of both sides gives us: \[ ...
Promotional Banner

Topper's Solved these Questions

  • CONTINUITY AND DIFFERENTIABILITY

    NCERT|Exercise EXERCISE 5.6|11 Videos
  • CONTINUITY AND DIFFERENTIABILITY

    NCERT|Exercise EXERCISE 5.2|10 Videos
  • CONTINUITY AND DIFFERENTIABILITY

    NCERT|Exercise QUESTION|3 Videos
  • APPLICATION OF INTEGRALS

    NCERT|Exercise EXERCISE 8.2|7 Videos
  • DETERMINANTS

    NCERT|Exercise EXERCISE 4.4|5 Videos

Similar Questions

Explore conceptually related problems

Differentiate x^(x) w.r.t. x.

Differentiate e^(x) w.r.t. sqrtx .

Differentiate x^(x^(x)) w.r.t. x.

Differentiate sin x w.r.t. cos x

Differentiate w.r.t x: y=tanx/x

Differentiate x^(2) w.r.t x^(3)

Differentiate x^(2) w.r.t cos x

Differentiate sin(x^(2)+x)w.r.t.x

Differentiate 3^(x) w.r.t.log(3x)

Differentiate (sin x)^(x) w.r.t. x.

NCERT-CONTINUITY AND DIFFERENTIABILITY-SOLVED EXAMPLES
  1. Prove that the function defined by f(x) = t a n xis a continuous func...

    Text Solution

    |

  2. Examine whether the function f given by f(x)=x^2 is continuous at x =...

    Text Solution

    |

  3. Discuss the continuity of the function f given by f(x) = |x| at x = 0.

    Text Solution

    |

  4. Check the continuity of the function f given by f(x) = 2x + 3 at x = ...

    Text Solution

    |

  5. Prove that the identity function on real numbers given by f(x) = x is...

    Text Solution

    |

  6. Is the function defined by f(x) = |x|, a continuous function?

    Text Solution

    |

  7. Show that the function f given by f(x)={x^3+3ifx!=0 ;1ifx=0 is not ...

    Text Solution

    |

  8. Check the points where the constant function f(x) = kis continuous.

    Text Solution

    |

  9. Discuss the continuity of the function/given by f(x)=x^3+x^2-1.

    Text Solution

    |

  10. Discuss the continuity of the function f defined by f(x)=1/x , x!=0.

    Text Solution

    |

  11. If y= A sin x+ B cos x, then prove that (d^2y)/(dx^2)+y=0.

    Text Solution

    |

  12. Find (d^2y)/(dx^2), if y=x^3+tanx.

    Text Solution

    |

  13. Find (dy)/(dx), if x^(2/3)+y^(2/3)=a^(2/3).

    Text Solution

    |

  14. Find (dy)/(dx), if x=a(theta+sintheta), y=a(1-costheta).

    Text Solution

    |

  15. Find (dy)/(dx), if x=a t^2, y=2a t.

    Text Solution

    |

  16. Find (dy)/(dx), if x=acostheta,y=asintheta.

    Text Solution

    |

  17. Find (dy)/(dx), if y^x+x^y+x^x=a^b.

    Text Solution

    |

  18. Differentiate x^(sinx), x >0w.r.t. x.

    Text Solution

    |

  19. Differentiate a^xw.r.t. x, where a is a positive constant.

    Text Solution

    |

  20. Differentiate sqrt(((x-3)(x^2+4))/(3x^2+4x+5)) w.r.t x.

    Text Solution

    |