How do you differentiate #g(x) =(x^2 + 6) (x^2 + 1)^5 # using the product rule?
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To differentiate the function g(x) = (x^2 + 6)(x^2 + 1)^5 using the product rule, follow these steps:
- Identify the two functions being multiplied: f(x) = x^2 + 6 and h(x) = (x^2 + 1)^5.
- Apply the product rule: g'(x) = f'(x)h(x) + f(x)h'(x).
- Differentiate f(x) with respect to x: f'(x) = 2x.
- Differentiate h(x) with respect to x: h'(x) = 5(x^2 + 1)^4 * 2x.
- Substitute the values into the product rule formula: g'(x) = (2x)(x^2 + 1)^5 + (x^2 + 6)[5(x^2 + 1)^4 * 2x].
- Simplify the expression if needed.
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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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