Question

what is its dy/dx without simplifying the answer?
1) sin x + sin y = 1
step by step please

Answer 1

implicit differentiation
you treat y as a function of x

cos x + cos y * dy/dx = 0

now make dy/dx the subject

Answer 2

I've applied the chain rule to sin y

Answer 3

sorry but still confused

Answer 4

Ok - you find the derivative term by term

derivative wrt x for sin x = cos x
derivative for the constant 1 is 0

ok?

Answer 5

wrt?

Answer 6

with respect to

Answer 7

oh ok

Answer 8

now for sin y we treat y as a function of x. The equation implies that.

Answer 9

so d/dx (sin(y(x))) = d/dx (1) then we differentiate term by term?

Answer 10

suppose y = x^2

we'd have sin x^2 and the derivative of that , by the chain rule is

d(x^2) / dx * d(sin x^2) / dx = 2x * cos x^2

Answer 11

but we have y not x^2 so we write dy/dx and cos y

Answer 12

ok thanks i got it

Answer 13

yw