# How do you differentiate #f(x)=x+1+(x+2)^2#?

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To differentiate ( f(x) = x + 1 + (x + 2)^2 ), you would use the rules of differentiation, particularly the power rule and the sum rule. First, differentiate each term separately, then sum the results. The derivative of ( x ) with respect to ( x ) is 1. The derivative of a constant (1) is 0. For the term ((x + 2)^2), apply the chain rule, which states that the derivative of ( u^n ) with respect to ( x ) is ( n \cdot u^{(n-1)} \cdot \frac{{du}}{{dx}} ). In this case, ( u = x + 2 ) and ( n = 2 ). The derivative of ( x + 2 ) is 1. So, the derivative of ((x + 2)^2) is ( 2 \cdot (x + 2)^{2-1} \cdot 1 = 2(x + 2) ). Therefore, the derivative of ( f(x) = x + 1 + (x + 2)^2 ) is ( f'(x) = 1 + 0 + 2(x + 2) = 2x + 5 ).

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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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