Differentiate the given function (two methods)
I only know how to do the chain rule which I get 8(4x-7)
please show how to do this so I can master the rest of the questions my self..thanks
$\displaystyle f(x)=(7-4x)(7-4x)$
I will differentiate it by product rule
$\displaystyle f'(x)=(7-4x)(-4)+(-4)(7-4x)=2(-4)(7-4x)$
in general
$\displaystyle f(x)=AB...A,B..functions..of..x$
differentiate
$\displaystyle f'(x)=A\frac{d}{dx}(B)+B\frac{d}{dx}(A)$
That is the product rule, the second equation is the differentiated form of your equation, and in the third Amer is showing you how to do it for any equation.
You take your original equation, reduce the power by 1, multiply the whole thing by the original power, this is the $\displaystyle 2$ in your equation, and then multiply the whole thing by the derivative of what's in the brackets, in your equation this is $\displaystyle (-4)$.
Hope this helps