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

We must use the chain rule:

Hence Differentiasting the 'outside' function, leaving the inside function as it is, then multiplying by the direvative of the 'inside' function...

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To find the derivative of the function ( f(x) = \sqrt{1 + 2x} ), you can use the power rule for differentiation, which states that the derivative of ( x^n ) with respect to ( x ) is ( nx^{n-1} ). Applying this rule, the derivative of ( \sqrt{1 + 2x} ) with respect to ( x ) is:

[ f'(x) = \frac{d}{dx}\left(\sqrt{1 + 2x}\right) = \frac{1}{2\sqrt{1 + 2x}} \cdot \frac{d}{dx}(1 + 2x) = \frac{1}{2\sqrt{1 + 2x}} \cdot 2 ]

[ f'(x) = \frac{1}{2\sqrt{1 + 2x}} \cdot 2 = \frac{1}{\sqrt{1 + 2x}} ]

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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.

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.

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.

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