How do you differentiate #f(x)=ln2x * cos3x# using the product rule?
Charles ArochaIt is
#(df(x))/dx=(d(ln2x))/dxcos3x+ln2x(d(cos3x))/dx=> (df(x))/dx=[((2x)')/(2x)]cos3x+ln2x(-sin3x)3=> (df(x))/dx=(cos3x)/x-3ln2xsin3x#
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Samantha AdkisonTo differentiate (f(x) = \ln(2x) \times \cos(3x)) using the product rule:
- Let (u = \ln(2x)) and (v = \cos(3x)).
- Compute (du/dx) and (dv/dx).
- Apply the product rule: [f'(x) = u'v + uv'] [f'(x) = (\frac{1}{x} \times \cos(3x)) + (\ln(2x) \times (-3\sin(3x)))]
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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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