DERIVATIVE OF A FUNCTION

DERIVATIVE OF A FUNCTION

DERIVATIVE

I.   Find the first derivative of the following functions.

    1.       f (x) = 2x⁴ – 8x³ 

    2.       f (x) = -4x² ( 4x² – 3)

    3.       f (x) = 5x^1/3 

    4.       f (x) = (3x³ – 4x)(5x²)

    5.       f (x) =  2 ( x² – 4) ^{– 2}

II.   Find the first and second derivative of the following functions.

    1.       f (z) = 8z⁴ – 10z³ 

    2.       f (x) = x² ( x² – 3)

    3.       f (z) = z^1/3

    4.       f (x) = (x³ – 2x)(3x²)

    5.       f (x) = ( x² – 4) ^{– 2}

III. Find the second derivative of the following functions.

     

    1.       f (x) = x⁵ + 3x³ – 4x² + 3

   

    2.       f (x) = x⁴/4 + x³/3 + x²/2 - x