What is the derivative of $y = {sec}^{3} (x)$ $y=sec^3(x)$ ?

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Answer 1 · 2014-07-25T21:18:23

Answer is

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

The solution is,

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

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

Similarly for the question asked above

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

What is the derivative of y=sec3(x)y=sec^3(x)?