How do you differentiate #f(x)=x+lnx^2-x^2# using the sum rule?
Rewrite using logarithm rules.
The sum rule simply means that you can take the derivative of each individual part and then add them together.
Thus,
Simplified:
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To differentiate ( f(x) = x + \ln(x^2) - x^2 ) using the sum rule, you differentiate each term separately.
- For ( x ), the derivative is ( 1 ).
- For ( \ln(x^2) ), the derivative is ( \frac{1}{x^2} \cdot 2x = \frac{2}{x} ).
- For ( -x^2 ), the derivative is ( -2x ).
So, the derivative of ( f(x) = x + \ln(x^2) - x^2 ) using the sum rule is ( f'(x) = 1 + \frac{2}{x} - 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.
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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