How do you graph the derivative of #f(x) = log (x)#?

Answer 1

See below.

First we need to find the derivative of #f(x)=log(x)#
#d/dx(log(x))=1/x#
as #x->0^-color(white)(88888)# ,#1/x->-oo#
as #x->0^+color(white)(888)# , #1/x->oo#

The y axis is a vertical asymptote.

as #x->oocolor(white)(88888)# ,#1/x->0#
as #x->-oocolor(white)(888)# ,#1/x->0#

The x axis is a horizontal asymptote.

GRAPH:

graph{y=1/x [-16.02, 16.01, -8.01, 8.01]}

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Answer 2

To graph the derivative of ( f(x) = \log(x) ), follow these steps:

  1. Find the derivative of ( f(x) ) using the differentiation rules. The derivative of ( \log(x) ) is ( \frac{1}{x} ).

  2. Plot the graph of ( \frac{1}{x} ) on the same coordinate system where ( x ) is positive, negative, and zero.

  3. The graph of ( \frac{1}{x} ) will have a vertical asymptote at ( x = 0 ) since division by zero is undefined.

  4. The graph will approach positive infinity as ( x ) approaches 0 from the positive side and negative infinity as ( x ) approaches 0 from the negative side.

  5. The graph of ( \frac{1}{x} ) will be decreasing for ( x > 0 ) and ( x < 0 ) since ( \frac{1}{x} ) is negative in these intervals.

  6. There will be no critical points since ( \frac{1}{x} ) has no points where its derivative is zero.

  7. Plot the graph according to these characteristics, and label the axes appropriately.

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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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