MHB How Do You Differentiate (1+sin²x)³?

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To differentiate (1 + sin²x)³, apply the chain rule. The derivative is calculated as 3(1 + sin²x)² multiplied by the derivative of the inner function, which is d/dx[1 + sin²x]. The inner derivative simplifies to 2sin(x)cos(x), leading to the final expression of 3(1 + sin²x)² * 2sin(x)cos(x). This method effectively demonstrates the application of the chain rule in calculus. Understanding these steps is crucial for mastering differentiation techniques.
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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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