SOLUTION: Using the function y=(4x^2-8x+3)^4 find y' using the chain rule(extended power rule)answer in the form y'=A(Bx^2-Cx+D)^e(fx-G) note all answers are integers which I got what is

Question 201612: Using the function
y=(4x^2-8x+3)^4 find y' using the chain rule(extended power rule)answer in the form y'=A(Bx^2-Cx+D)^e(fx-G)
note all answers are integers
which I got what is 4(4x^2-8x+3)^3 but can not figure out (fx-g) part and then it ask now use y' to find the equation of the tangent line at the point (2,81)
y=_________________ x-_____________
thanks

Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!
(Because of some limitations of the software on the Algebra.com site, I am doing to use dy/dx instead of y'.)
Let then
Substituting u into your equation we get

And, using the chain rule, we get

Substituting back in for both u and du/dx we get:

To find the equation of a tangent line (or any line) we need, in general, a point on the line and the slope for the line. We have the point, (2, 81). We need the slope. But y' gives us a formula for finding the slope of the tangent. We can use it to find the slope at x=2:

Squaring

Multiplying inside both parentheses

Adding and subtracting inside both parentheses

Cubing 3

Multiplying

Now we can use either the point-slope form or the slope intercept form to write the equation of the line through (2, 81) with a slope of 864. Using the point slope form we get:

If you need to have your answer in slope-intercept form, multiply

Then add 81

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