Differentiation question

Is this right? Can I or do I have to simplify it further?

*question*

You need to you the product rule:

if y = f(x)g(x)
y' = f'(x)g(x) + f(x)g'(x)

Where the ' means differentiated. So in this case let f(x) = cos^-1(x) and g(x) = sqrt(1-x^2) and you'll get the answer.

I think you're working was fine but then it seems like you've crossed out a + cos^-1(x), which would have made it correct (also as it is a function of t there should be no xs in your answer. You had differentiated sqrt(1-x^2) and cos^-1(x) correctly.

You need to you the product rule:

if y = f(x)g(x)
y' = f'(x)g(x) + f(x)g'(x)

Where the ' means differentiated. So in this case let f(x) = cos^-1(x) and g(x) = sqrt(1-x^2) and you'll get the answer.

I think you're working was fine but then it seems like you've crossed out a + cos^-1(x), which would have made it correct (also as it is a function of t there should be no xs in your answer. You had differentiated sqrt(1-x^2) and cos^-1(x) correctly.

One of us two misread the question ...

So I've made amendments. Is this right now?

if the question is to differentiate

ARCOS[√ (1-t²) ]

then I feel it is completely wrong

Yeah, that's the question. Where did I go wrong? I thought the derivative of arcos is what I wrote. The proof of it was here: [video="youtube;8YuSQq86_ro"]https://www.youtube.com/watch?v=8YuSQq86_ro[/video] Or did I write another step wrong?

first of all you had x and t

secondly there is no product, just a messy chain rule which incidentally was correct.

the differentiation should give

-1/√ [1 - (1 - t²] x .... the rest as you had on your first attempt.

your final answer should be

1/√ (1 - t²)

(maybe to be 100% correct multiplied by signum(t)

How did you get 1/√ (1 - t²) as the final answer?

Wouldn't -2t/2 = -t ? I got t/sqrt(1-t^2) as the answer.