# Implicit Differentiation w/ trig functions check

1. Oct 15, 2008

### DollarBill

1. The problem statement, all variables and given/known data
Determine dy/dx when

y*sin(x2)=5

3. The attempt at a solution
y*2xcos(x2) dx/dx + sin(x2)*1 dy/dx = 0

2xy cos(x2)*dy/dx = -sin(x2)

dy/dx = -sin(x2) / 2xy cos(x2)

dy/dx = -2xy tan(x2)

2. Oct 15, 2008

### Dick

How did 2xy magically pop from the denominator to the numerator?

3. Oct 15, 2008

### DollarBill

Would it be +2xy tan(x2)?

4. Oct 15, 2008

### STLCards002

y*2xcos(x2) dx/dx + sin(x2)*1 dy/dx = 0

2xy cos(x2)*dy/dx = -sin(x2)

What I notice is that you separated sin(x^2)dy/dx by subtraction..which is obviously "illegal"

Try isolating the term with dy/dx in it and then try to isolate just the dy/dx

5. Oct 15, 2008

### DollarBill

I didn't even notice I did that :yuck:

Working it out again:

y*2xcos(x2) dx/dx + sin(x2)dy/dx = 0

sin(x2)dy/dx = -2xycos(x2)

dy/dx = -2xycos(x2) / sin(x2)

dy/dx=-2xy*Cotx2

6. Oct 15, 2008

### Dick

That looks better.