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Answer: The derivative of the given function is 2/x. Example 3: Find the derivative of x ln x. Solution: Let f (x) = x ln x = x · ln x = u · v. By product rule, f' (x) = x d/dx (ln x) + ln x d/dx (x) Using ln derivative rules, the differentiation of ln x is 1/x and using the power rule, the derivative of x is 1. So.
Dec 21, 2020 · Use logarithmic differentiation to find this derivative. \(\ln y=\ln (2x^4+1)^{\tan x}\) Step 1. Take the natural logarithm of both sides. \(\ln y=\tan x\ln (2x^4+1)\) Step 2. Expand using properties of logarithms.
Derivatives Of Logarithmic Functions. The derivative of the natural logarithmic function (ln [x]) is simply 1 divided by x. This derivative can be found using both the definition of the derivative and a calculator. Derivatives of logarithmic functions are simpler than they would seem to be, even though the functions themselves come from an ...
For some derivatives involving ln(x), you will find that the laws of logarithms are helpful. In terms of ln(x), these state: Using these, you can expand an expression before trying to find the derivative, as you can see in the next few examples. Here, we will do into a little more detail than with the examples above. Example
Since the derivative of x with respect to x is 1, we can simplify the equation to: d/dx [ln x] = (d/dx) [ln(x)] * 1. Now, let’s find the derivative of ln(x) with respect to x. The derivative of ln x with respect to x is given by: (d/dx) [ln(x)] = 1/x. Therefore, the derivative of ln x is 1/x. In summary, the derivative of ln x is 1/x. More ...
The derivative rule for ln[f(x)] is given as: $$\frac{d}{dx}ln[f(x)] = \frac{f'(x)}{f(x)}$$ Where f(x) is a function of the variable x, and ' denotes the derivative with respect to the variable x. The derivative rule above is given in terms of a function of x. However, the rule works for single variable functions of y, z, or any other variable ...
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AboutAbout this video. Transcript. Let's explore the concept that the derivative of ln (x) is 1/x by examining the slopes of tangent lines at various points on the graph of y=ln (x). We'll observe that the slopes match the values of 1/x, reinforcing the statement. A future video will provide a proof for this concept.
