Trig Derivative - # 2

[Jason76]

\(\displaystyle y = \dfrac{8x}{1 - \cot x}\)

\(\displaystyle y' = \dfrac{[1 - \cot x][8]-[8x][-\csc^{2} x]}{(1 - \cot x)^{2}}\)

\(\displaystyle y' = \dfrac{[8 - 8 \cot x]-[-8 \csc^{3} x]}{(1 - \cot x)^{2}}\)

\(\displaystyle y' = \dfrac{[8(1 - \cot x)]-[-8 \csc^{3} x]}{(1 - \cot x)^{2}}\)

 

[stapel]

\(\displaystyle y = \dfrac{8x}{1 - \cot x}\)

\(\displaystyle y' = \dfrac{[1 - \cot x][8]-[8x][-\csc^{2} x]}{(1 - \cot x)^{2}}\)

\(\displaystyle y' = \dfrac{[8 - 8 \cot x]-[-8 \csc^{3} x]}{(1 - \cot x)^{2}}\)

\(\displaystyle y' = \dfrac{[8(1 - \cot x)]-[-8 \csc^{3} x]}{(1 - \cot x)^{2}}\)

Why are you factoring something out of some of the terms, rather than multiplying everything out to see what might combine or cancel off? What is your question regarding this exercise?

 

[Jason76]

Ok, let's look at his again:

\(\displaystyle y = \dfrac{8x}{1 - \cot x}\)

\(\displaystyle \dfrac{[1 - \cot x][8] - [8x][1 - (- \csc^{2} x)]}{(1 - \cot x)^{2}}\)

\(\displaystyle \dfrac{1 - \cot x][8] - [8x][1 + \csc^{2} x]}{(1 - \cot x)^{2}}\)

\(\displaystyle \dfrac{8 - 8\cot x - 8x - \csc^{2} x}{(1 - \cot x)^{2}}\) - This answer is still wrong on computer homework.

 

[Deleted member 4993]

Ok, let's look at his again:

\(\displaystyle y = \dfrac{8x}{1 - \cot x}\)

\(\displaystyle \dfrac{[1 - \cot x][8] - [8x][1 - (- \csc^{2} x)]}{(1 - \cot x)^{2}}\) ..................... Incorrect....\(\displaystyle \frac{d}{dx}[1-cot(x)] = cosec^2(x)\)

\(\displaystyle \dfrac{1 - \cot x][8] - [8x][1 + \csc^{2} x]}{(1 - \cot x)^{2}}\)

\(\displaystyle \dfrac{8 - 8\cot x - 8x - \csc^{2} x}{(1 - \cot x)^{2}}\) - This answer is still wrong on computer homework.

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[Jason76]

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Your answer is right. It checks out on computer homework.

\(\displaystyle y = \dfrac{8x}{1 - \cot x}\)

\(\displaystyle y' = \dfrac{[1 - \cot x][8]-[8x][-\csc^{2} x]}{(1 - \cot x)^{2}}\)

\(\displaystyle y' = \dfrac{8 - 8 \cot x - 8x -\csc^{2} x}{(1 - \cot x)^{2}}\)

 

[Deleted member 4993]

Your answer is right. It checks out on computer homework.

\(\displaystyle y = \dfrac{8x}{1 - \cot x}\)

\(\displaystyle y' = \dfrac{[1 - \cot x][8]-[8x][-\csc^{2} x]}{(1 - \cot x)^{2}}\) ................. Incorrect - it should be

\(\displaystyle y' = \dfrac{[1 - \cot x][8]-[8x][\csc^{2} x]}{(1 - \cot x)^{2}}\)

\(\displaystyle y' = \dfrac{8 - 8 \cot x - 8x * \csc^{2} x}{(1 - \cot x)^{2}}\)

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