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

Answer 1

Evelyn Agard

By the first derivative rule (and the simplest one): be #f(x)=x^n#, then #(df(x))/(dx)=n*x^(n-1)#

#(df(x))/(dx)=1*x^0+(1/2)*x^(-1/2)#

As everything times zero is zero and following a power rule that states that #a^-n=1/a^n#, we get:

#(df(x))/(dx)=1+1/(2x^(1/2))#

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Answer 2

Paisley Johnson

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