How do you use the chain rule to differentiate y=-2csc^6x?

1 Answer
Nov 21, 2017

dy/dx=dy/(dg)(dg)/dx, where g(x) is cscx

Explanation:

Make the substitution g(x)=cscx
y=-2g^6(x)

Now use the chain rule
dy/dx=dy/(dg)(dg)/dx
dy/(dg)=-12g^5(x)
(dg)/dx=(cscx)'=-cscxcotx
Plug these values in the initial equation
dy/dx=dy/(dg)(dg)/dx=-12g^5(x)g'(x)
dy/dx=12csc^5xcscxcotx
Therefore, the solution is
dy/dx=12csc^7xcosx