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How do you find the derivative of #1/(x-5)#?

Answer 1

Elijah Abram

Use #1/a=a^-1# and chain rule. It's #-1/(x-5)^2#

#1/(x-5)=(x-5)^-1#

The chain rule:

#((x-5)^-1)'=-1*(x-5)^(-1-1)*(x-5)'=#

#=-(x-5)^-2*1=-1/(x-5)^2#

Note: the chain rule does not make a difference in this case. However, if there was another function in which the denominator which didn't have a derivative equal to 1, the differentiation process would be more complex.

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Answer 2

Christopher Agresta

To find the derivative of $\frac{1}{x-5}$ , you can use the power rule for differentiation. The derivative is given by $-\frac{1}{{(x-5)}^2}$ .

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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.