Question
Asked Sep 26, 2019
57 views

Let exy = 2x + 4y + 2.

Use implicit differentiation to find the derivative of y with respect to x.

 

dy
dx

 = 

xA yB exy − C
D − xF yG exy

 , where

A = 
B = 
C = 
D = 
F = 
G =

check_circle

Expert Answer

star
star
star
star
star
1 Rating
Step 1

Given:

help_outline

Image Transcriptionclose

exy 2x4y + 2

fullscreen
Step 2

In implicit differentiation, we differentiate each side of an equation by treating one of the variables as a function of the other. We treat y as an implicit function of x.

help_outline

Image Transcriptionclose

Note: i) We use the chain rule to differentiate composite function: Iff and g are both differentiable and F = f'g (i.e. F(x) f(g(x)) is the composite function, then F'(x) f(g(x)) g'(x) ii) Product Rule: Iff and g are both differentiable, then d d d [f(x) g(x)f(x)g(x) + g(x) dx (f(x) dx = dx

fullscreen
Step 3

Now differentiate both side...

help_outline

Image Transcriptionclose

d d (2x4y 2) dx dx dy eху (ху) — 2+4 dx (Using the Chain Rule) dy х dx +y) dy (using the Product Rule) = 2 + 4- e*y dx Now, taking the derivative term to one side of the equation, dy (4 xe*y) yе*У — 2 dx уеху—2 dy dx 4-хеху

fullscreen

Want to see the full answer?

See Solution

Check out a sample Q&A here.

Want to see this answer and more?

Solutions are written by subject experts who are available 24/7. Questions are typically answered within 1 hour.*

See Solution
*Response times may vary by subject and question.
Tagged in

Math

Calculus

Derivative