18. if ( y = \tan x - cot x ), then ( dy/dx = )\na ( sec x csc x )\nb ( sec x - csc x )\nc ( sec x + csc x…

Explanation:

Step1: Recall derivative formulas

Recall that (\frac{d}{dx}(\tan x)=\sec^{2}x), (\frac{d}{dx}(\cot x)=-\csc^{2}x)

Step2: Differentiate (y = \tan x-\cot x)

Using the sum - difference rule (\frac{d}{dx}(u - v)=\frac{du}{dx}-\frac{dv}{dx}), where (u=\tan x) and (v = \cot x)

(\frac{dy}{dx}=\frac{d}{dx}(\tan x)-\frac{d}{dx}(\cot x))

Substitute the derivative formulas:

(\frac{dy}{dx}=\sec^{2}x-(-\csc^{2}x)=\sec^{2}x+\csc^{2}x)

Answer:

E. (\sec^{2}x+\csc^{2}x)