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Find equations of the tangent line and normal line to the curve at the given point.$ y = x^4 + 2e^x, (0,2) $

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01:38

Frank Lin

Calculus 1 / AB

Chapter 3

Differentiation Rules

Section 1

Derivatives of Polynomials and Exponential Functions

Derivatives

Differentiation

Missouri State University

University of Michigan - Ann Arbor

Idaho State University

Boston College

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.

00:57

Find equations of the tang…

02:38

02:24

it's clear. So when you right here. So we have y is equal to X to the fourth plus to eat tax. We're gonna differentiate, do you? I over d x and we get d over t X in terms of X for X to the fourth plus to eat the axe. This gives us four X cute plus to eat the axe in the slope of the tangent at zero comma, too. It is going to be, too, because when we plug in zero, this cross is out and this becomes just to so it's too. So the slope of the normal line has to be negative 1/2 since the product of slopes of perpendicular lines is negative. One. The tangent is the line. Passing through 02 was slope too. So the equation is lie minus two over X minus zero is equal to two. We get why it's equal to two acts plus two, and the normal is the line passing through 02 with slope negative 1/2. So the equation is boy minus two over X minus. Cerro is equal to negative 1/2. Why is equal to negative 1/2 X plus two. So this is our tangent, and this is our normal

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