How do you find the derivative of #f(x) = x + x^(1/2)#?

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Answer 1 · 2016-02-06T17:54:58

#f'(x)=1+1/(2x^(1/2)#

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)#