Question

Simple derivative function:

Answer 1

\[y=(sect+tant)^5\]

Answer 2

Chain rule again.
Once again, think of this:
\[\Large y = (\color{blue}{\sec t + \tan t })^5\]
as just one entity, differentiate as per the power rule... and then multiply the whole thing by the derivative of that 'entity'

Answer 3

Multiplication of the derivatives of layers (inner functions).

Answer 4

$$
\bf
\frac{d}{dx}(\sec(x) + \tan(x))^5\\\\
\text{Let u= }(\sec(x) + \tan(x))\\\\
\text{Then }\frac{du^5}{du}\frac{du}{dx}=5u^4\frac{du}{dx}\\\\
\frac{du}{dx}=\frac{d}{dx}(\sec(x) + \tan(x))=\sec^2(x))+\sec(x)\tan(x)\\\\
\text{So, }\frac{d}{dx}(\sec(x) + \tan(x))^5\\\\
=5(\sec(x) + \tan(x))^4(\sec^2(x))+\sec(x)\tan(x))\\\\
$$