what is the derivative of this function a=(7-2b)^3

a=(7-2b)^3  ...since this isn't too long, we could also expand it using the Binomial Theorem and then differentiate term by term...so we have

a = (7) - 3(7^2)*(2b) + 3(7)(2b)^2 - (2b)^3 

a = 7 - 294b + 84b^2 - 8b^3

da /db = -294 + 168b - 24b^2

a  =  (7 - 2b)³   --->   a'  =  3(7 - 2b)² · -2   --->    a'  =  -6(7 - 2b)²

My Ti-89 got  $${\mathtt{\,-\,}}\left({\mathtt{6}}{\mathtt{\,\times\,}}{\left({\mathtt{2}}{\mathtt{\,\times\,}}{\mathtt{b}}{\mathtt{\,-\,}}{\mathtt{7}}\right)}^{{\mathtt{2}}}\right)$$ . I am not sure why we are getting different answers. 

Last time I did calculus was in 2009. 

But here is a complete work through and a calculator you can use on line, which gave the same as my TI-89

https://www.symbolab.com/solver/derivative-calculator/%5Cfrac%7Bd%7D%7Bdb%7D%5Cleft(%5Cleft(7-2b%5Cright)%5E%7B3%7D%5Cright)/?origin=button

Hi Don,

Welcome to the Web2 forum   

The answers are identical

$$\\(7-2b)^2\\=((-1)*(2b-7))^2\\ = (-1)^2*(2b-7)^2\\=1(2b-7)^2\\=(2b-7)^2$$

an easier equivalent example is    

$$\\(8-3)^2=5^2=25\\ (3-8)^2=(-5)^2=25$$