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Find an equation of the tangent line to the curve at the given point.

$ y = x^2 \ln x, (1, 0) $

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00:47

Frank Lin

01:12

Doruk Isik

Calculus 1 / AB

Chapter 3

Differentiation Rules

Section 6

Derivatives of Logarithmic Functions

Derivatives

Differentiation

Campbell University

Oregon State University

University of Nottingham

Lectures

04:40

In mathematics, a derivative is a measure of how a function changes as its input changes. Loosely speaking, a derivative can be thought of as how much one quantity is changing in response to changes in some other quantity; for example, the derivative of the position of a moving object with respect to time is the object's velocity. The concept of a derivative developed as a way to measure the steepness of a curve; the concept was ultimately generalized and now "derivative" is often used to refer to the relationship between two variables, independent and dependent, and to various related notions, such as the differential.

44:57

In mathematics, a differentiation rule is a rule for computing the derivative of a function in one variable. Many differentiation rules can be expressed as a product rule.

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Find an equation of the st…

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Find an equation of the ta…

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02:33

0:00

in this problem, we have to find the equation for the tangent line to a curve and specifically were given a curve that is defined by a log rhythmic function. So we have the function. Why equals X square times the natural log of X and what we need to do before we confined the tangent line is find my prime. Well, how do we do that? We're going to have to apply the product rule. So why Prime would be equal to d X square dx times the national log of X plus x squared times d natural log of X over d x So when you do that, we simplify just a little bit. We get why prime equals two x times the natural log of X plus x So we have the derivative. But we want to know the equation for the tangent line. So what do we have to do now? We need the slope of our tangent line at the point that we're told in the problem 10 so we can plug in our X value into y prime. So why prime would be equal to two times one times the natural log of one plus one, so we would get zero plus one, which equals one. And now we confined the tangent line very easily. We have this form. Why? Minus why not equals M times X minus X not. And then we could just plug in the X and Y coordinates from our point, so we would have y minus zero equals one times X minus one, and then we can simplify to get the tangent line equals Why equal toe X negative one x minus one. Excuse me. So I hope that this problem helped you understand how we can find the tangent line to a curb using differentiation, specifically finding the derivative of a of a logarithmic function.

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