Implicit Differentiation w/ trig functions check

[DollarBill]

Homework Statement

Determine dy/dx when

y*sin(x²)=5

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)

 

[Dick]

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

 

[DollarBill]

Would it be +2xy tan(x²)?

 

[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

 

[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

 

[Dick]

That looks better.