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How do you differentiate #x+4/x#?

Answer 1

William Abdalla

#1-4/x^2#

Begin by expressing #x+4/x=x+4x^-1#

now differentiate using the #color(blue)"power rule"#

#rArrd/dx(x+4x^-1)=1-4x^-2=1-4/x^2#

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Answer 2

Adam Adkins

To differentiate (\frac{x + 4}{x}), you can use the quotient rule, which states that for a function (u/v), the derivative is ((u'v - uv')/v^2).

Let (u = x + 4) and (v = x). Then, (u' = 1) and (v' = 1).

Using the quotient rule, the derivative of (\frac{x + 4}{x}) is:

(\frac{(1)(x) - (x + 4)(1)}{x^2} = \frac{x - x - 4}{x^2} = \frac{-4}{x^2})

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Answer from HIX Tutor

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.