Find the derivative of fog(x) is f(x)= 2x-3 and g(x) = x^2-2

Given f(x)= 2x-3

g(x) = x^2
-2

We need to find
fog'(x)

First we need to determine the function
fog(x).

==> fog(x)= f(g(x) = 2g(x)
-3

                            = 2(x^2-3)
-3

==> fog(x) = 2x^2 -6 -3 = 2x^2
-9

==> fog(x)= 2x^2
-9

Now we will
differentiate.

==> fog'(x)=
4x

Then the derivative of fog(x) is fog'(x)=
4x