Question

𝐼𝑓 𝑦=𝑠𝑒𝑐^2 𝑥⁡ 𝑐𝑠𝑐^2 𝑥 ,𝑡ℎ𝑒𝑛: 𝑑𝑦/𝑑𝑥= …?

Answer 1

`(dy)/(dx)=-16cot2xcsc^3 2x`

Explanation:

As `y=sec^2xcsc^2x`

`y=1/(sin^2xcos^2x)=4/(sin^2 2x)=4csc^2 2x`

Hence using chain rule

`(dy)/(dx)=8csc2x*(-cot2xcsc2x)*2`

= `-16cot2xcsc^2 2x`

Answer 2

`dy/dx = - (16cos 2x)/sin^3 (2x)`

Explanation:

You can simplify the expression in the following way:

`y = sec^2x csc^2x = 1/cos^2x 1/sin^2x = 1/(sinxcosx)^2 = 4/(sin^2 2x)`

Then:

`dy/dx = - (16cos 2x)/sin^3 (2x)`