How do you find the derivative of #f(x) = x + sqrt(x)#?

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Answer 1 · 2017-05-18T05:41:00

#1+sqrt(x)/(2x)#

Chain Rule is not needed here. Just use thee Power Rule.

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

Answer 2 · 2017-05-18T05:51:15

Use algebra and the power rule.

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

When #f(x) = x^n#, the power rule states that the derivative follows the trend #f'(x) = nx^(n-1)#.

Applied to your specific problem...

#f(x) = x + sqrt(x)#

(Use your knowledge of algebra to rewrite the root as an exponent...)

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

(Now just take the derivative by using the power rule...)

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