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Use the properties of logarithms to find the derivative. Hint: It might be easier if you use the properties of logarithms first.$$y=\ln x^{6}$$

$$6 / x$$

Algebra

Chapter 4

Exponential and Logarithmic Functions

Section 6

Properties of Logarithmic Functions

Campbell University

Oregon State University

Baylor University

Lectures

01:18

Use the properties of loga…

02:09

01:46

01:13

01:22

02:15

01:06

02:22

02:07

01:59

01:11

03:11

01:44

Use logarithmic differenti…

02:55

Okay, So our task is to find the derivative of natural log of X to the six power and the law of logs that they want you to do is taking this power and moving this in front. And then when you take the derivative of this, I think it makes perfect sense. He wide the X that the six is just the constant that kind of goes along for the ride. And then the drift of a natural log of X is one over X. You could just stick that into the denominator s. So this is the correct answer. And just to prove that, that's the right answer. What you could have done instead is the chain rule where the drift of would be won over the drift of natural log is one over that function. But then times the derivative of the inside, which is six x to the fifth. And you know, if I were to do you know exponents rules, you'd see that there's five X is in the numerator. There's six X is in the denominator. Well, five of them canceled. You left was six over X. You're correct. Answer. So we did it right

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