Question

differentiate y=x^tan 3x

Answer 1

is that \(y=x^{\tan3x}\)?

Answer 2

I find these to be simpler to think about if I change it around to this:
\[y=x^{\tan3x}=e^{\ln(x)\tan(3x)}\]

Answer 3

yess

Answer 4

indeed, @Kainui is correct.

Answer 5

$$y=x^{\tan(3x)}\\\log(y)=\tan(3x)\log(x)\\\frac{d}{dx}\log(y)=\frac{d}{dx}[\tan(3x)\log(x)]\\\frac1y\frac{dy}{dx}=\frac{d}{dx}[\tan(3x)]\cdot\log(x)+\tan(3x)\cdot\frac{d}{dx}[\log(x)]\\\frac1y\frac{dy}{dx}=3\sec^2(3x)\log(x)+\frac1x\tan(3x)\\\frac1{x^{\tan(3x)}}\frac{dy}{dx}=3\sec^2(3x)\log(x)+\frac1x\tan(3x)\\\frac{dy}{dx}=3x^{\tan(3x)}\sec^2(3x)\log(x)+\frac{x^{\tan(3x)}}x\tan(3x)\\\frac{dy}{dx}=3x^{\tan(3x)}\sec^2(3x)\log(x)+x^{\tan(3x)-1}\tan(3x)$$

Answer 6

bump -- no feedback? :-(

Answer 7

Remember whenever we have a funtion^function, take log on both sides. This helps us to attack the question :)

Answer 8

hey i just saw your answer @oldrin.bataku :)

Answer 9

np @fatinazmi -- remember to reward the most helpful response with a medal

Answer 10

we can substitute back 1/y with y=x^tan 3x?

Answer 11

yep :)

Answer 12

y was a variable we made .So we should replace it in the final answer.

Answer 13

okay. thank you everyone. really helpful :)