MYTUTOR SUBJECT ANSWERS

654 views

How do I find dy/dx for the following equation: (x^2) + 2y = 4(y^3) + lnx?

This is an example of implicit differentiation with respect to x.

The technique for differentiating such an equation is as follows:

1. Differentiate each term in x with respect to x.

2. For each term in y, differentiate with respect to y, and multiply the result by dy/dx.

3. Rearrange the resulting equation, to make dy/dx the subject of the formula.

Solution:

Let equation (x^2) + 2y = 4(y^3) + lnx be called (*).

Differentiating (*) with respect to x, then rearranging, according to the three rules above, gives:

2x + 2(dy/dx) = [12(y^2)](dy/dx) + (1/x) =>

[2 - 12(y^2)](dy/dx) = (1/x) - 2x =>

2[1 - 6(y^2)](dy/dx) = [1 - 2(x^2)]/x =>

dy/dx = [1 - 2(x^2)]/(2x[1 - 6(y^2)]).

 

Caleb O. GCSE Maths tutor, A Level Maths tutor, Uni Admissions Test M...

2 years ago

Answered by Caleb, an A Level Maths tutor with MyTutor


Still stuck? Get one-to-one help from a personally interviewed subject specialist

253 SUBJECT SPECIALISTS

£20 /hr

Jacob F.

Degree: Mathematics (Bachelors) - Warwick University

Subjects offered:Maths, German+ 2 more

Maths
German
Further Mathematics
-Personal Statements-

“2nd year Maths undergrad with enhanced DBS (CRB) certification and experience teaching in secondary schools and at University. Fluent German speaker.”

Aisling R. A Level Maths tutor, A Level Chemistry tutor
£20 /hr

Aisling R.

Degree: Chemistry (Bachelors) - Bristol University

Subjects offered:Maths, Chemistry

Maths
Chemistry

“Top tutor from the renowned Russell university group, ready to help you improve your grades.”

£20 /hr

Harry D.

Degree: Mathematics with a year abroad (Masters) - Sheffield University

Subjects offered:Maths

Maths

“My name is Harry, I am a Mathematics student at the University of Sheffield. I am very enthusistic about the subject and love to help others improve their skills. I am a well organised, patient and friendly individual and I feel these ...”

About the author

Caleb O. GCSE Maths tutor, A Level Maths tutor, Uni Admissions Test M...

Caleb O.

Currently unavailable: for regular students

Degree: BSc Discrete Mathematics (Bachelors) - Warwick University

Subjects offered:Maths, Music

Maths
Music

“Excellent mathematics and music tutor, seeking to explain concepts clearly to students”

You may also like...

Other A Level Maths questions

What is a derivative?

Edexcel January 2007 - Question 4 (Rates and Differential Equations)

Express 2/P(P-2) in Partial Fractions (C4)

x^2 + y^2 + 10x + 2y - 4xy = 10. Find dy/dx in terms of x and y, fully simplifying your answer.

View A Level Maths tutors

We use cookies to improve your site experience. By continuing to use this website, we'll assume that you're OK with this. Dismiss

mtw:mercury1:status:ok