Hello everyone. I am in need of help for some of my online practice problems. I typed them up on Microsoft Word as well as my work, and was hoping for further assistance.
For the first one, it isn't the composition of three functions you have, it's the product of two functions, 5x
and cos(x˛), one of which is the composition of two functions (the latter). Also you'll need to find the 2nd
derivative. For the second one, correct. Well done. Just cancel the 13's for simplification's sake, perhaps.
I'm just wondering, how do you find out what the composition actually is? That is probably my biggest problem; figuring out how I should split up the problem.
Thank you. I'm always worried when I simplify because sometimes I don't replace the values with something equivalent and mess everything up.
Are you clear on exactly what a "composition" of two functions is? It means something of the form f(g(x)), not just any combination of functions like, say f(x)g(x).
Here, you had the function $\displaystyle 5x cos(x^2)$. The $\displaystyle x^2$ is inside the cos( ) so that is a composition. The "5x" and "cos(x)" are not inside any function of a single variable, they are multiplied together. That is why it is wrong to say you have a "composition of three functions". You have the product of two functions, 5x, and $\displaystyle cos(x^2)$ for which you want to use the product rule and then a composition: $\displaystyle cos(x^2)= cos(y)$ with $\displaystyle y= x^2$.
Thank you. I'm always worried when I simplify because sometimes I don't replace the values with something equivalent and mess everything up.[/QUOTE]
Wow total flop on my part, my mind was still partially thinking of the product rule.
But now, wouldn't I be in a similar situation as the original function? This new function derived from the chain rule is of very similar format to the original function.