- #26

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[itex]\frac{1}{\sqrt{2}}[/itex] as cos π/4 or sin π/4 ?What is [itex]\frac{1}{\sqrt{2}}[/itex]? Can you write it in a trigonometric form?

And expand cot(x) as cos(x)/sin(x).

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- #26

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[itex]\frac{1}{\sqrt{2}}[/itex] as cos π/4 or sin π/4 ?What is [itex]\frac{1}{\sqrt{2}}[/itex]? Can you write it in a trigonometric form?

And expand cot(x) as cos(x)/sin(x).

- #27

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Do you know the definition of derivative of a function in limit form? Question (2) is the simple definition of derivative of f(y) in that form. All you need to do is find what f(y) is and then find f'(y).OMG..sorry...it's not x to a ,but x to 0....sorry

- #28

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urgh..then its the derivative of ysec(y)....so then ?Do you know the definition of derivative of a function in limit form? Question (2) is the simple definition of derivative of f(y) in that form. All you need to do is find what f(y) is and then find f'(y).

Is it the answer ?-ysec(y) ?

- #29

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Yes, the answer is theurgh..then its the derivative of ysec(y)....so then ?

Is it the answer ?-ysec(y) ?

- #30

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We have not such rule in Limits but in differential calculus we were taught,Yes, the answer is thederivative ofy*sec(y). But you need to apply product rule while differentiating this function!!

y=f(x)g(x)

[itex]\frac{dy}{dx}[/itex]=g(x)f'(x)+f(x)g'(x)

- #31

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Exactly. Use this rule to differentiate y*sec(y), that's the answer you are looking for!We have not such rule in Limits but in differential calculus we were taught,

y=f(x)g(x)

[itex]\frac{dy}{dx}[/itex]=g(x)f'(x)+f(x)g'(x)

- #32

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what about the [3] one?

- #33

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Convert [itex]\frac{1}{\sqrt{2}}[/itex] into [itex]cos(\frac{\pi}{4})[/itex], and apply the formula that changes the difference of two trigonometric terms into their product. In the denominator, after writing cot in terms of cos and sin, try getting a single trigonometric ratio and simplify.what about the [3] one?

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