derivatives: f(x) = 6sqrt(x) + cosx, (x^3 - 3x^2 + 4)/(x^2)

[chao2006]

the exercise is to find the derivative of the function
I dont understand why further in the problem the 6 turns into a 3. f(x)= 6?x + cosx I understood until the last step were the 6 turn into a 3?

xˆ3-3xˆ2+4 the second one i didn't understand how to slove at all the book had I very different answer from mine. I did the problem over ,but I still dont have what the answer book does.
xˆ2

I thought I could distribute the xˆ2 and cancel the middle exponent.

 

[wjm11]

the exercise is to find the derivative of the function
I dont understand why further in the problem the 6 turns into a 3. f(x)= 6?x + cosx I understood until the last step were the 6 turn into a 3?

xˆ3-3xˆ2+4 the second one i didn't understand how to slove at all the book had I very different answer from mine.
x^2

The ?x expression can be written as x^(1/2), so

f(x)= 6?x + cosx = 6x^(1/2) + cosx

f’(x) = (1/2)(6)(x)^(-1/2) – sinx

For the second problem, use the quotient rule.