# What is the derivative of y=sec^3(x)?

Jul 25, 2014

$y ' = 3 \cdot {\sec}^{2} x \cdot \sec x \cdot \tan x$

The solution is,

For problems like these, $y = f {\left(x\right)}^{n}$

then $y ' = n \cdot f {\left(x\right)}^{n - 1} \cdot f ' \left(x\right)$ (this is the Power Chain Rule)

Similarly for the question asked above

$y ' = 3 \cdot {\sec}^{2} x \cdot \sec x \cdot \tan x$