Show the differentiation

Differentiate each of the following with respect to x.

i)-7 cosex(2 - x^4) ............................answer : -28x^3cosec(2-x^4)cot(2-x^4)
ii) 2 tan(x^3 - 6x^2)................................ans… : 6x(x-4)sec^2(x^3 - 6x^2)


Can you people help me to solve those question? i was confused with the working i mean i might find a way to solve this but come out with a different answer. So i need the help form you people to show me the correct working to solve this. thanks!

i) let y = -7cosec(u), where u = 2 - x^4

=> dy/du = 7cosec(u)cot(u) and du/dx = -4x^3

the chain rule states that dy/dx = (dy/du)(du/dx)

=> dy/dx = -28x^3cosec(2 - x^4)cot(2 - x^4)

ii) let y = 2tan(u), where u = x^3 - 6x^2

=> dy/du = 2sec^2(u) and du/dx = 3x^2 - 12x

=> dy/dx = 6x(x - 4)sec^2(x^3 - 6x^2)

:)>

i)I assume you mean -7cosec(2-x^4)
Let u=2-x^4 so y=-7cosecu
The chain rule states dy/dx=(dy/du)(du/dx)
dy/du=7cosecucotu , du/dx=-4x^3
so dy/dx=-28x^3cosecucotu= answer

ii) Let u=x^3-6x^2 so y=2tanu and use chain rule again,
dy/dx=(dy/du)(du/dx)=2sec^2(u)(3x^2-12…

Click on this link and then click Show Steps there. Now thank me very much.
http://www.wolframalpha.com/input/?i=differentiate+-7+cosec%282+-+x%5E4%29

-7 x 4x^3 cosex(2-x^4)cot(" ...") --- product rule