How Do You Differentiate (1+sin²x)³?

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SUMMARY

The differentiation of the function (1 + sin²x)³ requires the application of the chain rule. The first step involves applying the chain rule to obtain 3(1 + sin²x)² multiplied by the derivative of the inner function, which is d/dx[1 + sin²x]. This process simplifies the differentiation task and leads to the final derivative expression. The discussion emphasizes the importance of mastering the chain rule for complex functions.

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can someone go through the steps how to differentiate (1+sin²x)³
 
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markosheehan said:
can someone go through the steps how to differentiate (1+sin²x)³
It's multiple uses of the chain rule:
[math]\frac{d}{dx} [ (1 + sin^2(x) )^3 ] [/math]

[math]= 3 (1 + sin^2(x) )^2 \cdot \frac{d}{dx} [ 1 + sin^2(x) ] [/math]

Can you finish from here?

-Dan
 
yes thanks
 

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