Derivative of a complex function: F(x)=((x-7) / (x+2))^2 F'(x)=?

Answer 1

First, use the chain rule, combined with the power rule:
d/dx[(g(x))^n] = n[g(x)]^(n-1)*g'(x)

Then,
F'(x) = 2[(x-7)/(x+2)] * d/dx[(x-7)/(x+2)]

For the last part, use the quotient rule:

d/dx[(x-7)/(x+2)] =
[(x+2)d/dx(x-7) - (x-7)d/dx(x+2)] / (x+2)^2 =
[(x+2) - (x-7)] / (x+2)^2 =
9/(x+2)^2.

Put it all together:

F'(x) = 18(x-7)/(x+2)^3.

Answer 2

F'(x) = 2 * [(x-7)/(x+2)] * [(x-7)/(x+2)]'

[(x-7)/(x+2)]' = 9/(x+2)²

=> F'(X) = 18*(x-7) / (x+2)^3

Answer 3

Expand the function

F(x) = (x-7)^2/(x+2)^2

expand the (x-7)^2 and then break it into a sum to get
F(x) = (x^2 -14*x +49) / (x+2)^2
or
F(x) = (x^2)/(X+2)^2 ...
If you make the denominator negative two, then you can use the product rule.

Upon simplification you get
F'(x) = 18*(x-7) ...

but you can figure out the rest of that expression on your own.

Answer 4

Just use the quotient rule. This function is very simple, not complex.