Question

No idea how to do this one :(

Answer 1

\[f(x)=(\arctan(6x^{2}+5))^{2}\]

Answer 2

not sure if i have to simplify then get the derivative or what. no idea.

Answer 3

What are the exact instructions for this problem?

Answer 4

Find f'(x) for the following functions

Answer 5

f^(6)(0) = -10/9.

Answer 6

huh?

Answer 7

Refer to the attachment.

Answer 8

Arctan is the inverse os tan, so \[\tan\left(\pm \sqrt{f(x)}\right)=6x^2+5\]Now take the derivative on both sides and an f' will appear. Isolate it and you get your answer.

Answer 9

what is that link? is it a website?

Answer 10

i dont understand the second step in the attachment

Answer 11

Its mathematica or wolfram|alpha, but the website does that too, but it can be very confusing and it does not always give you the best way of solving.

Answer 12

is that the best way to solve my question though?

Answer 13

It is, as long as you remember the formula for the derivative of arctan. Its up to you if you want to remember a lot of formulas or not. If you don't I sugest trying another way, the way I said before probably works, and the only things you have to remember are the derivatives for polinomials, wich is basic and derivatives of trig functions cos and sin wich are also basic. But if you know that formula the other way is better, no doubt.

Answer 14

so that way wasn't with the formula, how do i do it with the formula?

Answer 15

With the formula is the picture from mathematica.

Answer 16

Without the formula is like this:\[f(x)=\arctan^2(6x^2+5)\]\[\tan\left(\pm \sqrt{f(x)}\right)=6x^2+5\]Derivating on both sides you get:\[\left[1+\tan^2\left(\pm \sqrt{f(x)}\right)\right]\left(\pm\frac{1}{2\sqrt{f(x)}}\right)f'(x)=12x\]\[\left[1+\tan^2\left(\pm \arctan(6x^2+5)\right)\right]\left(\pm \frac{1}{2\arctan(6x^2+5)}\right)f'(x)=12x\]\[\pm \frac{1+(6x^2+5)^2}{2\arctan(6x^2+5}f'(x)=12x\]\[f'(x)=\pm \frac{24x \arctan(6x^2+5)}{1+(6x^2+5)^2}= \frac{24x \arctan(6x^2+5)}{1+(6x^2+5)^2}\]We choose the positive sign because the negative sign does not make sense considering the function you have.

Answer 17

i wanted to know how to do it with the formula.

Answer 18

with the formula is normal chain rule, its done in the picture the guy posted above

Answer 19

that explanation is as clear as it gets