



 
Erson, This is an exercise with using the chain rule. The key is to realize that cos^{3}x is another way to write (cosx)^{3}. Hence you differentiate cos3x much the same way you would differentiate (x^{2}  7x + 9)^{3}. So let's do it. If y = (x^{2}  7x + 9)^{3} then to find y' you first notice that y = (something)^{3} and you know how to differentiate something raised to the third power because if
But my function, y = (x^{2}  7x + 9)^{3} isn't quite that simple, it's y = (something)^{3} and the chain rule tells me that
But I know the derivative of x^{2}  7x + 9, its 2x  7. Thus what I have is that if
then
Now you try this with y = cos^{3}x = (cosx)^{3}. Harley  


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