Expert: Paul Klarreich - 10/17/2006

Question
Hi Paul,

I cant seem to finish off the following maths sum.

Find the slope of the tangent to the curve
x sin y + y^2 = 1 + (PI^2/4) at the point
(1, PI/2)

I used implicit differentiation and product rule:

x.cos y(dy/dx) + siny.1 + 2y(dy/dx) = 0

x.cos y(dy/dx) + 2y(dy/dx) = -siny

(dy/dx) = -siny / xcosy + 2y

then put in (1, PI/2)

(dy/dx) = -sin(PI/2) / 1.cos(PI/2) + 2(PI/2)

Sin(PI/2) = 0 and Cos(PI/2) = 0 therefore

(dy/dx) = 0 / 0 + PI which is equal to 0

But the answer is meant to be -1/PI

Where have i gone wrong?  

Answer
Annie Asks in Category Advanced Math ...
 
Subject:  Implicit Differentiation
Private:  no
 
Question:  Hi Paul,

I cant seem to finish off the following maths sum.

Find the slope of the tangent to the curve
x sin y + y^2 = 1 + (PI^2/4) at the point
(1, PI/2)

I used implicit differentiation and product rule:

x.cos y(dy/dx) + siny.1 + 2y(dy/dx) = 0

x.cos y(dy/dx) + 2y(dy/dx) = -siny

(dy/dx) = -siny / xcosy + 2y

then put in (1, PI/2)

(dy/dx) = -sin(PI/2) / 1.cos(PI/2) + 2(PI/2)

Sin(PI/2) = 0 and Cos(PI/2) = 0 therefore
.........HERE IS THE ERROR ..........
>> Oops.  You got one of those wrong:

sin pi/2 = 1  and  cos pi/2 = 0.

Try it now.
....................................

(dy/dx) = 0 / 0 + PI which is equal to 0

But the answer is meant to be -1/PI

Where have i gone wrong?