# Calculus

posted by .

find y' if sin^-1(xy)=cosy

• Calculus -

Use implicit differentiation:
sin^-1(xy)=cosy
sin(cos(y))=xy
differentiate both sides with respect to x
(use chain rule):
cos(cos(y))(-sin(y))y'=y+xy'
Collect terms and solve for y'
y'=-y/(cos(cos(y))sin(y)+x)

## Similar Questions

1. ### calc

what is the derivative of sinx- cosy = 0 in its simplest form?
2. ### Calculus

Consider the function f(x)=sin(1/x) Find a sequence of x-values that approach 0 such that sin (1/x)=0 sin (1/x)=1 sin (1/x)=-1 Is sin sin (1/x)=0 and sin (1/x)=-1 does not exist. What is sin (1/x)=1 then.
3. ### integral Calculus

ʃsin y dy/ √1 + cosy please help..thanks.. that's integration of sin y dy divided by (over) square root of 1 + cosy.
4. ### Pre-calculus

If cosx=4/5, cosy=12/13 in Quad. IV, find sin(x+y)
5. ### Pre-calculus

If cosx=4/5, cosy=12/13 in Quad. IV, find sin(x+y)
6. ### Trigonometry Help

Simplify: sin(x-y)cosy+cos(x-y)siny = (sinxcosy-cosxsiny)cosy+(cosxcosy+sinxsiny)siny = ?
7. ### math

Suppose e^y=sin(x+cosy) Find dy/dx using implicit differentiation
8. ### Math

Suppose f(x) = sin(pi*cosx) On any interval where the inverse function y = f –1(x) exists, the derivative of f –1(x) with respect to x is: a)-1/(cos(pi*cosx)), where x and y are related by the equation (satisfy the equation) x=sin(pi*cosy) …
9. ### Math

If X and Y are in the interval (0,pie/2) and sin x =3/2 and cosy =12/13 evaluate each of the following a)sin(x-y)
10. ### math

Knowing that 0 <= x <= pi/2, 0 <= y <= pi/2, that sinx = 1/4 and that cosy = 1/5, find sin(x + y), sin(x - y), cos(x + y), cos(x - y)

More Similar Questions