Question

y = e^cotx^2

Answer 1

find y'

Answer 2

Could you show us what you've done so far with the question please?

Answer 3

find y' if \[y = e ^{\cot x ^{2}}\]

Answer 4

Derivative of e^(u) = e^(u) * u'.

Answer 5

i know the derivative of \[e ^{u}\] = eu (u')

Answer 6

So do you know that if you differentiate e to the something, the derivative will contain the same term.

Answer 7

would i use u substitution?

Answer 8

Okay. So if you differentiate
\[e^{\cot x^2}=e^{\cot x^2}\times \frac{dy}{dx}(\cot x^2)\]

Answer 9

\[\frac{d}{dx}*\]

Answer 10

\[e ^{cotx ^{3}} \times -\csc ^{2}x\]

Answer 11

Then you have to differentiate x^2.

Answer 12

And that derivative of cotx^2 seems a bit wonky.

Answer 13

\[\large \frac{d}{dx} \cot x^2=-\csc^2 x^2 \times \frac{d}{dx}x^2\]

Answer 14

Do you understand that? or are you a bit muddled up with that?

Answer 15

i have to apply the chain rule and keep taking the derivative til i reach the last term?

Answer 16

i get it.

Answer 17

yes, that is why it is called the "chain" rule!

Answer 18

So, can you show me your full answer please?

Answer 19

\[-2x \csc ^{2}x e ^{cotx ^{2}}\]

Answer 20

uhh, there's a small error in that answer. there should be an x^2 inside csc^2

Answer 21

ohh .. ok

Answer 22

Do you understand your error or confused why you got that wrong?

Answer 23

yes .. because i took the derivative of cotx^2

Answer 24

Yep. WEll done. It seems you did it. Congratulations.

Answer 25

thank you

Answer 26

No worries.