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Find $\frac{d y}{d x}$ if $y=\frac{3-5 x}{x+3}$

$-18 /(x+3)^{2}$

Calculus 1 / AB

Chapter 2

An Introduction to Calculus

Section 5

Derivative Rules 2

Derivatives

Harvey Mudd College

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.

30:01

In mathematics, the derivative of a function of a real variable measures the sensitivity to change of the function value (the rate of change of the value of the function). If the derivative of a function at a chosen input value equals a constant value, the function is said to be a constant function. In this case the derivative itself is the constant of the function, and is called the constant of integration.

01:05

Find $\frac{d y}{d x}$.

00:48

$$ \text { If } y=3 x+5, \…

02:02

Find $d y / d x$.$$

01:07

$$\text {Find } D_{x} y$$ …

01:17

find $d y / d x .$ $y=…

01:15

00:40

00:49

02:13

Find $d y / d x$$$…

So our task is to find the derivative of this quotient rule. You can tell it's a quotient rule because it's a giant questions. Yeah, that's clever. So we have three minus five x over X plus three. So everyone write that down. If you see a quotient, that's what that division is. And we have to do the quotient rule. Well, what is the quotient rule that is taking the derivative off the top. While the derivative of three is zero, the derivative of negative five X is negative. Five. You leave X plus three alone minus. Now you take the derivative of the bottom, which is one, and then you leave the top alone. Three minus five x all over the denominator squared. Now, some teachers, we'll let you leave your answer like this. You know, when they're happy and they move on, other teachers will say Nope. You got to distribute. Okay, well, if you distribute so just in the new numerator you get negative. Five X minus 15 minus three plus five x. I think you could tell that those exes will cancel and negative 15 minus three gives me negative 18. So this is the best answer over X plus three squared. Oops.

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