Question

What is the derivative of sqrt(1 + sec(x)^4) ?

Answer 1

\[f(x) = \sqrt{1+\sec^4x}\]
use the chain rule, taking \(y= \sec ^4 x\) then,

\[f(y)= \sqrt{1+y}\]
\[\frac{d f(x)}{dx} = \frac{df(y)}{dy}\frac{dy}{dx}= \frac{d[\sqrt{1+y}]}{dy}\frac{d(\sec^4 x)}{dx}\]

to find \(\frac{d\sec^4 x}{dx}\) you can again use the chain rule (hint : take \(t = \sec x\))