How do you find the derivative of #f(x) = x + x^(1/2)#?
1 Answer
Feb 6, 2016
Explanation:
The thing you must know here is the power rule, which states that
#d/dx(x^n)=nx^(n-1)#
We can differentiate each term individually:
#f'(x)=d/dx(x^1)+d/dx(x^(1/2))#
Applying the power rule to each of these gives:
#f'(x)=1x^(1-1)+1/2x^(1/2-1)#
Simplify.
#f'(x)=1x^0+1/2x^(-1/2)#
#f'(x)=1+1/(2x^(1/2)#
This can also be written as
#f'(x)=1+1/(2sqrtx)#
