Sorry, I just couldn't find out by my self
Anyone got a clue for these three question?
f(x) = (x^2 - 24) / (x+2)
y= ln(x tan x)
I know it looks very simple but I'm totally lost.
Please give me a hint for those two ,
Thank you.
Sorry, I just couldn't find out by my self
Anyone got a clue for these three question?
f(x) = (x^2 - 24) / (x+2)
y= ln(x tan x)
I know it looks very simple but I'm totally lost.
Please give me a hint for those two ,
Thank you.
For these sorts of problems, you have to kind of "reverse the order" of evaluation. Take f(x) = (x^2 - 24) / (x+2). The last arithmetic operation you would do in evaluating the function at a point would be the division. Therefore, that's the first thing you differentiate. What is the quotient rule?
For the second function, you work from outside in. You'll need the chain rule as well as the product rule. What do you get?
Your answer to the first question is correct, but ONLY if you put in parentheses like so:
(x^2+4x+24)/(x+2)^2. To use a better-looking format, your answer is this:
$\displaystyle x^2+4x+\dfrac{24}{(x+2)^{2}},$ whereas the correct answer is this:
$\displaystyle \dfrac{x^{2}+4x+24}{(x+2)^{2}}.$ They are not the same!
For the second problem, I don't think you understand yet. What is the chain rule? How does it apply here? What is the outermost function?
Yeah, that's looking better. I would probably write the answer as
$\displaystyle \dfrac{\tan(x) + x \sec^{2}(x)}{x\tan(x)}.$
Then it's perfectly clear what is in the argument of each trig function, and what's in the numerator and denominator of the fraction.