How do you find the first and second derivative of #ln(x/20)#?

Answer 1

#d/(dx) ln(x/20) = 1/x#

Based on the properties of logarithms:

#ln(x/20) = lnx -ln20#

so that:

#d/(dx) ln(x/20) = d/(dx) ln(x) = 1/x#
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Answer 2

We use the Rule #ln(a/b)=lna-lnb,# and get, #y=lnx-ln20.#

#:." The First Derivative "y'=(lnx)'-(ln20)'=1/x-0#

#=1/x=x^-1.#

#"Next, since, "(x^n)'=nx^(n-1)," the Second Derivative "y''#

#=(y')'=(x^-1)'=-1x^(-1-1)=-1/x^2#.

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Answer 3

To find the first derivative of ln(x/20), apply the chain rule: (1/(x/20))*(1/20). Simplify to get 1/x.

To find the second derivative, differentiate the first derivative: -1/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.

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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