# Thread: Implicit differentiation

1. ## Implicit differentiation

Hi,

Q1. Find derivative of cos(x+y) + y = 0

could anyone give me steps and the answer for this please?

thanks,

moon

2. Originally Posted by Moon Hoplite
Hi,

Q1. Find derivative of cos(x+y) + y = 0

could anyone give me steps and the answer for this please?

thanks,

moon
If y is a function of x, then :
$\cos(x+y)$ has to be differentiated following the chain rule.
$[\cos(u(x))]'=-u'(x) \sin(u(x))$

So the derivative of $\cos(x+y)=-(1+y') \sin(x+y)$

So the derivative of $\cos(x+y)+y=0$ is $-(1+y')\sin(x+y)+y'=0$