How do you differentiate #g(x) =x^2tanx# using the product rule?
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g'(x) =
# x^2sec^2x + 2xtanx #
applying the rule of the product:
g'(x) = f(x).h'(x) + h(x).f'(x) is the result if g(x) = f(x).h(x).
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To differentiate ( g(x) = x^2 \tan(x) ) using the product rule, follow these steps:
- Identify the two functions within the product: ( f(x) = x^2 ) and ( h(x) = \tan(x) ).
- Differentiate ( f(x) ) with respect to ( x ) to get ( f'(x) ).
- Differentiate ( h(x) ) with respect to ( x ) to get ( h'(x) ).
- Apply the product rule: ( g'(x) = f(x)h'(x) + f'(x)h(x) ).
- Substitute the derivatives and the original functions back into the formula to find ( g'(x) ).
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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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