f(x)=(25-x^2)^(1/2)dx, similar problem will be used on taylor polynomial exam. can somebody tell me if there is a easier way of taking the function up to it's 3rd derivative without spending so much time doing all the calculations.

Question

anonymous · Answer

you kind of just have to do the derivative 3 times. do you want to see it

anonymous · Answer

Is the given function
$$f(x)=\int\sqrt{25-x^2}~dx~~\text{or}~~f(x)=\int_0^x\sqrt{25-t^2}~dt~~?$$

anonymous · Answer

no, it's just f(x)=(25-x^2)^(1/2)dx, so i have to take it to the 3rd derivative to used it to do taylor patrimonial

anonymous · Answer

Are you telling me it's not even an integral?

anonymous · Answer

no it's not, sorry there shouldn't be a dx at the end, i think that's what caused the confusion

anonymous · Answer

Okay. Well, what's so bad about taking the derivative three times? I can't say there's a quick and easy way to just compute the derivatives other than using a calculator.

anonymous · Answer

i was told that it will be on a exam with just different numbers, so i don't want to waste time doing all the work ....i can't even find a similar problem on the book, that's why i'm wondering