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

Expert Answers
hala718 eNotes educator| Certified Educator

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

justaguide eNotes educator| Certified Educator

We have f(x)= 2x-3 and g(x) = x^2 - 2

fog(x) = f(g(x))

=> f( x^2 - 2)

=> 2*(x^2 - 2) - 3

=> 2x^2 - 4 - 3

=> 2x^2 - 7

The derivative of 2x^2 - 7 = 4x

The required derivative is 4x.