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Find the slope of a line tangent to the curve of $y=x \ln 3 x$ at $x=4$ Verify the result by using the numerical derivative feature of a calculator.

Calculus 1 / AB

Chapter 27

Differentiation of Transcendental Functions

Section 5

Derivative of the Logarithmic Function

Derivatives

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Campbell University

Harvey Mudd College

Idaho State University

Lectures

03:09

In mathematics, precalculu…

31:55

In mathematics, a function…

01:08

Find the slope of the tang…

01:43

01:30

01:10

01:24

04:06

04:41

01:59

02:06

07:57

Find the equation of the t…

Okay, so we want to find a soap of our tangent line, human or expertly. So that's a car. Slope is equal to F prime of a, which is equal to this equation here. So let's start by finding definitely, since you already have of X, so after May is equal to, um, that's going to be our A value is for so yet Fourth Word, which is equal to 16 and I'll. It's also find X minus a, which is a denominator. So here we have just x minus four. So let's rewrite this as the limit as X approaches for, uh, X squared minus 16 over. Excellent it's for no, it's no in our numerator. This is the difference of two squares. So we concocted this into X minus four times X plus war. And now let's cancel out our like times. I know you contracts up yet four plus four, which is equal to eight

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