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

Answer 1

Ezekiel Alexander

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)#

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Answer 2

Emma Aldridge

#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)#

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Answer 3

Paisley Johnson

To find the derivative of ( f(x) = x + \sqrt{x} ), you can use the power rule and the chain rule. The derivative is ( f'(x) = 1 + \frac{1}{2\sqrt{x}} ).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.