How do you differentiate #g(x) = sqrt(2x^2-1)cos3x# using the product rule?
The formula for the product rule is
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To differentiate g(x) = √(2x^2 - 1) * cos(3x) using the product rule:
- Let u(x) = √(2x^2 - 1) and v(x) = cos(3x).
- Find the derivatives of u(x) and v(x): u'(x) = (4x) / (2√(2x^2 - 1)) and v'(x) = -3sin(3x).
- Apply the product rule: g'(x) = u(x)v'(x) + v(x)u'(x).
- Substitute the values obtained in steps 2 and 3 into the product rule formula.
g'(x) = (√(2x^2 - 1))(-3sin(3x)) + (cos(3x))((4x) / (2√(2x^2 - 1)))
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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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