Question

Question #487b1

Answer 1

Use the quotient rule as detailed in the explanation. Solution at end of explanation.

Explanation:

To evaluate this we use the quotient rule, which states:

`y(x)=(f(x))/(g(x)), dy/dx = ((df)/dxg(x) -f(x)(dg)/dx)/(g(x))^2`

We have here the following:

`f(x) = 8x, (df)/dx = 8, g(x)=1-tan(x), (dg)/dx= -sec^2(x)`

Then we have:

`dy/dx = (8(1-tanx)-(-8xsec^2x))/((1-tan2x)^2) = (8(xsec^2x-tanx+1))/(1-tanx)^2`
`=(8xsec^2x)/(1-tanx)^2 + 8/(1-tanx)`