Question

Find the derivative of f(x):

Answer 1

\[f(x) = \sqrt[5]{\frac{ 3x^3 \tan(x^3-5x^2+3x-10) }{ (5x^2+1)^3 }}\]

Answer 2

WOW!! So do you have to do the chain rule, then quotient rule mixed with more chain rules and the product rule mixed with chain rules.

Is this really a question you need help with or a general post to the community.

Answer 3

Do you know the final answer?

Answer 4

I don't, but I have my answer.

Answer 5

dude its 2 LOOOOOOOOOOOOOOONG

Answer 6

My Brain

Answer 7

we knowed, the answer too long...
so, i just give a hint :)
y = (f(x))^1/5
y' = f '/{5*[(f(x))^(4/5)]}, hehe...

Answer 8

\[f(x) = (\frac{ 3x^3 \tan(x^3-5x^2+3x-10) }{ (5x^2+1)^3 })^{(1/5)}\]\[\color{blue}{\frac{1}{5}}(\frac{ 3x^3 \tan(x^3-5x^2+3x-10) }{ (5x^2+1)^3 })^{\color{blue}{(-4/5)}}*\text{derivative of inside}\]Derivative of Inside:\[\[\frac{ \color{green}[3x^3 \tan(x^3-5x^2+3x-10)\color{green}{]'}\color{red}[(5x^2+1)^3\color{red}{]-[}3x^3 \tan(x^3-5x^2+3x-10)\color{red}]\color{purple}{[}(5x^2+1)^3\color{purple}{]'} }{ \color{red}((5x^2+1)^3\color{red}{)^2} }\]That's the quotient rule, but now we have to mix in the product rule in order to take the green derivative and the chain rule for the purple derivative

Green Part: \[\color{green}[3x^3 \tan(x^3-5x^2+3x-10)\color{green}{]'}\]\[3x^3\sec^2(x^3-5x^2+3x-10)*(3x^2-10x+3)+9x^2\tan(x^3-5x^2+3x-10)\]Purple Part:\[\color{purple}{[}(5x^2+1)^3\color{purple}{]'}\]\[3(5x^2+1)^2*(10x)\]

I'll leave it to you to replace the parts and simplify the denominator

Answer 9

\[\color{red}{-[}3x^3 \tan(x^3-5x^2+3x-10)\color{red}]\color{purple}{[}(5x^2+1)^3\color{purple}{]'} \]This is the part that was cut off. starting from the negative sign

Answer 10

Log differentiation. I didn't do that.... :/

Answer 11

Logrithmic differentiation just seem'd easier to do for me than using product, quotient, chain, etc.,
I am putting your answer together tho right now to compare.

Answer 12

I can't remember how to do log differentiation, I as forced to do the long way. Nothing is simplified in my answer above

Answer 13

Haha. For working the problem with me. I am still simplifying ur answer. Lol

Answer 14

This is a hell of a problem

Answer 15

http://en.wikipedia.org/wiki/Logarithmic_differentiation

I looked it up, this method is way easier. I'm kinda sry to put you through trying to get my answer in the same form.

Answer 16

It's not a problem at all man! No need to be sorry.
I should be the one saying sorry for putting up such a difficult problem.

Answer 17

wolframalpha is god

Answer 18

Can't use Wolframalpha during exams.

Answer 19

Yeah but you can while checking your answer from an old exam. http://www.wolframalpha.com/input/?i=d%2Fdx((((3x%5E2tan(x%5E3-5x%5E2%2B3x-10))%2F(5x%5E2%2B1)%5E3)%5E(1%2F5))&t=crmtb01