Question

Find the derivative of y=(sin^-2) (x^3)

Answer 1

Hi cmkc109 :)
does your question look like\[\large y=\frac{1}{\sin^2(x^3)}\]where x^3 is the angle of sine. right?

Answer 2

yes.. it is sin ^-2 (x^3)
so it is the same as what u wrote there

Answer 3

ohh..i actually dont know..i thought it is like a product rule or something.. is x^3 suppose to be the angle or sin..

Answer 4

No. it is not a product rule. but a chain rule must be use here. OK.

Answer 5

ohh..can u still guide me how to do it..still confuse on trig derivatives

Answer 6

sure friend :)
\[\large y=\frac{1}{\sin^2(x^3)}\]derivative with respect to x\[\large \frac{d}{dx}(y)=\frac{d}{dx}(\frac{1}{\sin^2(x^3)})\]\[\large \frac{dy}{dx}=\frac{d}{dx}(\sin^{-2}(x^3))\]\[\large \frac{dy}{dx}=(-2)(\cos^-3(x^3))\frac{d}{dx}(x^3)\]\[\large \frac{dy}{dx}=(-2)(\frac{1}{\cos^{3}(x^3)})(3x^2)\]\[\large \frac{dy}{dx}=\frac{-6x^2}{\cos^3(x^3)}\]

Here you go buddy :)

Answer 7

thank you my friend :D

Answer 8

you are ever welcome :)