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We need to find the composition F of G of X.
So if we have F of U and we're given that U is G of X.
So now we know F of G of X.
But we're given that G of X is 6 square roots of X.
So now it's F of six square roots of X.
So now we're going to put six square roots of X into the F
equation every time we see our unknown.
So cosine PI6 square roots of X / 24 that inside parenthesis
will simplify to Pi 4 sqrt X.
Now we need the derivative of cosine which is negative sine.
Then we need to take the derivative of the inside piece
and the derivative of the inside piece is going to be Pi 4 * 1 /
2 sqrt X.
So simplifying that up, we get negative π / 8 sqrt X sine Pi 4
sqrt X.
It specifies we want to know what happens at X equal 4.
So now we're just going to stick 4IN for our XS.
We get negative π / 8 * 2 or negative π sixteenths.
Sine Π force times sqrt 2, sorry times sqrt 4, which is 2.
So sine of π halves.
Sine of π halves is one for a final answer.
Answer of negative π sixteenths.