Sometimes easy and sometimes hard, our calculus problem of the week could come from any calculus topic. If you really want to get better at calculus, following these problems is a great way to make yourself practice! Past calculus problems of the week.
This week’s problem:
(click “see the solution” at the bottom of post to, well, see the solution.)
Suppose you know the following information about two functions:
Use this information to find ![[f(g(2))]'](https://s0.wp.com/latex.php?latex=%5Bf%28g%282%29%29%5D%27&bg=ffffff&fg=000&s=0&c=20201002)
is a composite function, so to find the derivative you should use the chain rule. Applying the chain rule here would give us ![[f(g(x))]'=f'(g(x))\cdot g'(x)](https://s0.wp.com/latex.php?latex=%5Bf%28g%28x%29%29%5D%27%3Df%27%28g%28x%29%29%5Ccdot+g%27%28x%29&bg=ffffff&fg=000&s=0&c=20201002)
. Therefore ![[f(g(2))]'=f'(g(2))\cdot g'(2)=f'(2)g'(2)=7\cdot (-3)=-21](https://s0.wp.com/latex.php?latex=%5Bf%28g%282%29%29%5D%27%3Df%27%28g%282%29%29%5Ccdot+g%27%282%29%3Df%27%282%29g%27%282%29%3D7%5Ccdot+%28-3%29%3D-21&bg=ffffff&fg=000&s=0&c=20201002)
Notice that if it wasn’t true that 
