You are here:

# Advanced Math/Calculus AB question - implicit differentiation

Advertisement

Question
Hello Mr. Ahmed,

I have a multiple choice question and I am getting the derivative, but my answer choice is not listed in the problem. Hereis the problem I a struggling with:

If tan(xy)=x, then dy/dx=

A. (1-ytan(xy)sec(xy))/(xtan(xy)sec(xy))
B. (sec^2(xy)-y)/x
C. cos^2(xy)
D. (cos^2(xy))/x
E. (cos^2(xy)-y)/x

Thank you so much for your time!

Nikita

Answer
Hi Nikita,
To make it easier, let z = xy
Now,
tan(z) = x
differentiating, we get
secē(z) . dz/dx = 1
but from z = xy
dz/dx = x.dy/dx + y
Therefore,
secē(xy) . (x.dy/dx + y) = 1
x.dy/dx + y = 1/secē(xy)
x.dy/dx + y = cosē(xy)
x.dy/dx = cosē(xy) - y
dy/dx = [cosē(xy) - y] / x

Regards
Questioner's Rating
 Rating(1-10) Knowledgeability = 10 Clarity of Response = 10 Politeness = 10 Comment No Comment

• Add to this Answer
• Ask a Question

Advanced Math

All Answers

Ask Experts

Volunteer

#### Ahmed Salami

##### Expertise

I can provide good answers to questions dealing in almost all of mathematics especially from A`Level downwards. I can as well help a good deal in Physics with most emphasis directed towards mechanics.

##### Experience

Aspiring theoretical physicist. I have been doing maths and physics all my life.

Education/Credentials
I teach mathematics and engineering physics.

©2017 About.com. All rights reserved.

Browse Answers:

[an error occurred while processing this directive]