B Don't follow one small step in proof

[SamRoss]

https://www.wyzant.com/resources/lessons/math/calculus/derivative_proofs/inverse_trig

The above link is just a proof for the derivative of arcsinx. Going from line 3 to 4, how does d/dx siny become dy/dx cosy ?

 

[andrewkirk]

https://www.wyzant.com/resources/lessons/math/calculus/derivative_proofs/inverse_trig

The above link is just a proof for the derivative of arcsinx. Going from line 3 to 4, how does d/dx siny become dy/dx cosy ?

It is applying the rule for derivative of a function of a function. This is more apparent if we write it as $\frac d{dx}\sin(y(x))$.

 

[SamRoss]

It is applying the rule for derivative of a function of a function. This is more apparent if we write it as $\frac d{dx}\sin(y(x))$.

So it's just the chain rule. Can't believe I missed that. Thanks for your help!