Question

y=e ^tan^-1 ^2

Answer 1

\[\large y=e^{\tan^{-1}x^{2}} \]

Answer 2

chain of three. the e function, the tan^-1 function, and the x^2 function. three factors for dy/dx.

Answer 3

its too complicated,i dont know where to start lol :|

Answer 4

I tend to start with the most outside perpective and work my way in... the first function to consider is e^(something)... the derivative is e^(something) times the derivative of the something.

Answer 5

yes i know that i dont know what after that!

Answer 6

Then chain on the derivative of the inverse tangent with that x squared still in it, then chain on the derivative of the x squared.

Answer 7

the derivative of \[\large e^{tan^{-1}x^2}\]is \[\large e^{tan^{-1}x^2}\] that is our first on the chain of factors

Answer 8

yes

Answer 9

the derivative of \[\large tan^{-1}x^2\]is \[\large \frac{1}{1+(x^2)^2}\] the second part of the chain

Answer 10

the third part is the derivative of x^2

Answer 11

just "chain" the derivatives by multiplication

Answer 12

like this?
\[\large e^{\tan^{-1}x^{2}} \times e^{1+x^{2}} \times e^{2x}\]

Answer 13

there is no e on the 2nd and third factors, just the first factor, like this \[\large e^{\tan^{-1}x^2} \times \frac{ 1 }{ 1+(x^2)^2 } \times 2x\]

Answer 14

okay!clear!