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IgorLugansk [536]
3 years ago
15

What is the derivative of y=tan(arcsin(x))?

Mathematics
1 answer:
Anuta_ua [19.1K]3 years ago
4 0
Hello,

(tg(x))'=1/cos²(x)

(arcsin(x))'=1/√(1-x²)

cos²(arcsin(x))=1-sin²(arcsin(x))=1-x²


(tg(arcsin(x)))'= \dfrac{1}{cos(arcsin(x)))^2} * \dfrac{1}{\sqrt{1-x^2}} \\

=\dfrac{1}{1-sin(arcsin(x))^2}* \dfrac{1}{\sqrt{1-x^2}} \\

= \dfrac{1}{1-x^2} * \dfrac{1}{\sqrt{1-x^2}} \\

\boxed{= \dfrac{\sqrt{1-x^2}}{x^4-2x^2+1}}\\


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Answer:

let a = x² (a ≥ 0), we have the equation:

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Answer: $4110.8 (more likely - 95% sure) or $2,107 (less likely)

Step-by-step explanation: It could be $4110.8 because you have the take the total they made and subtract is from the cost of the toys ($7,230-$2,450=$4,780). Then you have to take the result of that and get 14% of it, then subtract that from the $4,780 amount. Then you get the final answer which is $4110.8.

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However, it could also be $2,107 because the question itsn't that clear in the second sentence. It could be saying that $2,450 is the price of the toys (which is what I assumed above), or that it is the profit that the $2,450 (which I used below). I think that the above answer is more likely because if not then the first number would never be used. Anyways here is the second way it could be.

Step-by-step explanation: It could be $2,107 because you take the profit ($2,450) and get 14% of it, then subtract that from the $2,450 amount. Then you get the final answer which is $2,107.

If I was you, I would do the first one ($4110.8) because I really think it is that one. I just put the other one here just in case.

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