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In summary, the conversation discusses using Latex to type formulas on a website, but the person is having trouble with the formatting. They also mention a solution to a problem involving the chain rule in differentiation.

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Here is how to type formulas on PF (it's not difficult):

https://www.physicsforums.com/help/latexhelp/

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$$\tfrac{dy}{dx}=\tfrac{( \cos x)^{\sin y}\sin y \tan x - ( \sin x)^{\cos y}\cos y \cot x}{( \cos x )^{ \sin y } \cos y \log \cos x - ( \sin x) ^{\cos y} \sin y \log \sin x}$$

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Ahh, I apologise.fresh_42 said:

Here is how to type formulas on PF (it's not difficult):

https://www.physicsforums.com/help/latexhelp/

I've tried using Latex as you have asked, but I'm afraid it's taking way too long to type out my working.

However, I've taken a better photo, I'm not confident in my working but please do check. Thank you :)

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Thank you for the answer. But may I ask what working you've done to solve this?benorin said:

$$\tfrac{dy}{dx}=\tfrac{( \cos x)^{\sin y}\sin y \tan x - ( \sin x)^{\cos y}\cos y \cot x}{( \cos x )^{ \sin y } \cos y \log \cos x - ( \sin x) ^{\cos y} \sin y \log \sin x}$$

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The chain rule should be used when the function being differentiated is composed of two or more functions, where one function is nested within the other. This can be identified by looking for expressions such as f(g(x)) or g(f(x)).

The formula for applying the chain rule in implicit differentiation is d/dx(f(g(x))) = f'(g(x)) * g'(x). This means that the derivative of the outer function is multiplied by the derivative of the inner function.

Yes, the chain rule can be applied to any function that is composed of two or more nested functions. This includes polynomial, exponential, logarithmic, and trigonometric functions.

When differentiating a function with a constant, the constant can be treated as a coefficient and can be factored out of the derivative. For example, if the function is y = 3x^2, the derivative would be dy/dx = 6x.

One common mistake is forgetting to apply the chain rule to both the inner and outer functions. It is important to differentiate each function separately and then multiply them together. Another mistake is not properly simplifying the final expression after applying the chain rule.

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