Differentiate \(\frac{x}{cosx}\) with respect to x
A
1 + x sec x tan x
B
1 + sec2 x
C
cos x + x tan x
D
x sec x tan x + secx
Verified Correct Answer: D.
Step-by-Step Mathematical Solution
let y = \(\frac{x}{cosx}\) = x sec x ( since \(\frac{1}{cosx}\) = sec x )
let u = x, v = sec x
\(\frac{dy}{dx}\) = U\(\frac{dy}{dx}\) + V\(\frac{du}{dx}\)
\(\frac{dy}{dx}\) = x [secx tanx] + secx
Therefore, \(\frac{dy}{dx}\)\(\frac{x}{cosx}\) = x secx tanx + secx
Source: Myschool Past Questions Archive (Record #30738)