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vova2212 [387]
3 years ago
11

Michelle baby-sits the neighbors' children. She watches the Rogers' child for $5 per hour

Mathematics
1 answer:
mixas84 [53]3 years ago
4 0

Answer:

What is the objective to answer the question? Is it how much they will get?

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Derivatives of inverse trigonometric functions please explain answers
Jobisdone [24]

I'll explain how to do the first one:-

y = cos-1(x2)

This can be described as ' a function of a function'   x^2 is a function of x and cos-1(x^2) is a function of x^2.

We need to  apply the chain rule.

Personally I find this  easier to understand if i let u = x^2, so

If y = f(u) and u is a function of x then

dy/dx = dy/ du * du/dx

Here u = x^2  and y = cos-1(u)

du/dx = 2x

so dy/dx = d(cos-1(x^2) dx = dy/du * du/dx


= -1 / √(1 - u^2) * 2x

= -2x / √(1 - u^2)    

= -2x / √(1 - (x^2)^2)

= -2x / √(1 - x^4)

I hope this helps. but if not. you might like to employ the formulae in the question - The square boxes contain the 'u' s in my answer. These formulae are equivalent to my explanation.

6 0
3 years ago
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