menu
bartleby
search
close search
Hit Return to see all results

What is ln(x+2y)=x^4 using implict differentiation to find the derivative of y with respect to x?

Question

What is ln(x+2y)=x^4 using implict differentiation to find the derivative of y with respect to x?

check_circleAnswer
Step 1

Given function:

In(x2y) x4
help_outline

Image Transcriptionclose

In(x2y) x4

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.

Note: We use the chain rule to differentiate composite function:
Iff and g are both differentiable and F fg (i.e. F(x) f(g(x))) is the
composite function, then
F'(x) f'(g(x))g'(x
help_outline

Image Transcriptionclose

Note: We use the chain rule to differentiate composite function: Iff and g are both differentiable and F fg (i.e. F(x) f(g(x))) is the composite function, then F'(x) f'(g(x))g'(x

fullscreen
Step 3

Now, we differentiate th...

n(x 2y) x4
Differentiate with respect to x
d
d
- (In(x2y))
(x4)
dx
dx
1
(x 2y)
dx
4x3
(Using the chain rule.)
X+2y
1
4x3
(2y)
1 +
x+2y
[(1+2)
dy
1
4x3
. (This is because we treat
dx.
X+2y
y as a function of x.)
4x3 (х + 2y) — 1
dy
dx
2
help_outline

Image Transcriptionclose

n(x 2y) x4 Differentiate with respect to x d d - (In(x2y)) (x4) dx dx 1 (x 2y) dx 4x3 (Using the chain rule.) X+2y 1 4x3 (2y) 1 + x+2y [(1+2) dy 1 4x3 . (This is because we treat dx. X+2y y as a function of x.) 4x3 (х + 2y) — 1 dy dx 2

fullscreen

Want to see the full answer?

See Solution

Check out a sample Q&A here.

Want to see this answer and more?

Our solutions are written by experts, many with advanced degrees, and available 24/7

See Solution
Tagged in

Math

Calculus

Derivative

Sorry about that. What wasn’t helpful?