Calculus Examples

$y = \ln (x - x)$

Step 1

Write $y = \ln (x - x)$ as a function.

$f (x) = \ln (x - x)$

Step 2

Find the first derivative of the function.

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Step 2.1

Subtract $x$ from $x$ .

$\frac{d}{d x} [\ln (0)]$

Step 2.2

Since $\ln (0)$ is constant with respect to $x$ , the derivative of $\ln (0)$ with respect to $x$ is $0$ .

$0$

Step 3

Since $0$ is constant with respect to $x$ , the derivative of $0$ with respect to $x$ is $0$ .

$f'' (x) = 0$

Step 4

To find the local maximum and minimum values of the function, set the derivative equal to $0$ and solve.

$0 = 0$

Step 5

Since there is no value of $x$ that makes the first derivative equal to $0$ , there are no local extrema.

No Local Extrema

Step 6

No Local Extrema

Step 7