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 said: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 ?
So it's just the chain rule. Can't believe I missed that. Thanks for your help!andrewkirk said: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)) ##.
Not following one small step in proof means that in the process of proving something, a key step or piece of evidence is ignored or left out. This can lead to an incomplete or incorrect conclusion.
Missing a step in proof can lead to an invalid or flawed conclusion. Just like a puzzle, if one piece is missing, the entire picture may be distorted or incomplete.
To avoid missing steps in proof, it is important to carefully and thoroughly follow a logical and systematic approach. Double-checking and reviewing the evidence and steps taken can also help catch any potential errors or omissions.
The consequences of not following one small step in proof can vary depending on the situation. In some cases, it may lead to an incorrect conclusion or result. In others, it may create confusion or mistrust in the validity of the proof.
It depends on the specific situation. If the missing step is caught early on, it may be possible to go back and correct it. However, if the error is not discovered until later on, it may require starting over from the beginning or may even be impossible to fix.