What is the derivative of #x^(3/2)#?
1 Answer
Explanation:
If you have already learnt the concepts of differentiating, skip to the solutions instead.
Differentiation of power functions is found as
By differentiating a function, you are decreasing its power/exponent by 1.
Imagine you are given a cube with its corner lengths being
The volume of this cube will be
Thus, let the volume be
The result is
#V'(x)=3x^2 cm^2#
Notice we differentiate both the function and its unit.
Now, its power has decreased to 2, and its unit is now cm squared instead of cm cubed.
By differentiating, the cube has been reduced from having 3 dimensions to just 2 dimensions.
The cube has been reduced to just a surface of the cube (or plane) ie changed from cube to a square.
If we differentiate again,
#V''(x)=6x cm^1#
Its power is reduced to 1, and reduced to just a line from a square.
So what happens when we differentiate
Which is basically nothing (zero).
Try practicing differentiating the volume of a sphere,
Solution
#=(3/2)x^(1/2)#
Differentiating rational powers of functions ie
Can you imagine what happens by differentiating functions with irrational powers ie