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

$f'(x)=1+1/(2sqrtx)$

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