Download the App!

Get 24/7 study help with the Numerade app for iOS and Android! Enter your email for an invite.

Question

Answered step-by-step

(a) Find $ y' $ by implicit differentiation.(b) Solve the equation explicitly for y and differentiate to get $ y' $ in terms of $ x. $(c) Check that your solutions to part (a) and (b) are consistent by substituting the expression for $ y $ into your solution for part (a).

$ \sqrt{x} + \sqrt{y} = 1 $

Video Answer

Solved by verified expert

This problem has been solved!

Try Numerade free for 7 days

Like

Report

Official textbook answer

Video by Doruk Isik

Numerade Educator

This textbook answer is only visible when subscribed! Please subscribe to view the answer

01:38

Frank Lin

Calculus 1 / AB

Chapter 3

Differentiation Rules

Section 5

Implicit Differentiation

Derivatives

Differentiation

Baylor University

University of Michigan - Ann Arbor

Idaho State University

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.

08:24

(a) Find $y^{\prime}$ by i…

02:43

(a) Find $ y' $ by im…

09:05

02:22

03:46

04:14

09:31

02:07

04:04

02:35

06:11

In this problem were given an equation, wording equation is of x, plus the root of y is equal to 1. In part, a we asked to use implicit differentiation to find very to function y. So let's stood out. Let'S take derivative of all the terms with respect to x. Preston would give us 1 over 2 square root of x. Plus second term would give us 1 over 2 square. Now we're in to inner function since y is also a function of have dx and that is equal to 0, because 1 is just a constant. So let's leave the i d x on the 1 side we have y t is then equal to negative 1. Over 2 star root of x, divided by 1 over 2 square root. I means to would cancel out and you would find the answer as the negative of y divided by s x now in part b, were asked to explicitly solve for y and then take derivative of that function. So we see that square root of y is equal to 1 minus square root of x. Now, if we take square of sides, we find y to be 1 minus square root of x. Squared now, let's find which of this y prime is equal to 2 times 1 minus square root of x times the roof inner function, which is negative 1 over 2 square root of x and 2, will cancel out and we find then the answer to be negative. So square root of x, minus 1 give i by square root of x all right now in part c, we are asked to compare the derivative we find in part and part b. So, let's take derivative of the function y that we find in part a so we have negative of the root of y divided by the square root of x. Now, in part, we find what our function y is, and from this we see that y is equal to negative of square root of 1 minus square root of x square square, root, divided by square x, square root and square will cancel out and will end up With negative of 1 minus square root of x, divided by square root of x, and that is equal to square root of x, minus 1 divided by square and as you can see, this is same as what we had for. So we can see that you can say that both implicit and explicit differentiation gi us the same result.

View More Answers From This Book

Find Another Textbook

03:02

The graph below shows the function yand four rectangles The top right co…

01:28

For each statement, choose if it is simple or compound. If it is compound, c…

04:50

A sinusoid e cOS @t can be expressed as sum of exponentials e" and e wi…

01:43

Suppose that 6 cards are draw fromn well-shuffled deck of 52 cards_ What is …

09:51

Use an appropriate infinite series method about X 0 to find two solutions of…

08:57

Consider the initial value problem for the vector-valued function xX-3 x…

03:04

QUESTION 12 The mileages recorded for a sample of company vehicles during a …

02:33

Solar Panel Power Output The graph of the function shown In the accompanying…

01:02

A presidentia candidate plans to begin her campaign by visiting the capitals…

01:39

Question 20.5pCsIna study of crime; the FBI found that 13.2% of all …