Question #62094

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Answer 1 · 2016-03-02T11:49:54

$\frac{d}{d x} ({sec}^{2} x) = 2 {sec}^{2} x tan x$ $d/dx(sec^2x)=2sec^2xtanx$

The derivative of $sec x$ $secx$ is $sec x tan x$ $secxtanx$ .

$[1] \frac{d}{d x} ({sec}^{2} x)$ $[1]" "d/dx(sec^2x)$

$[2] = \frac{d}{d x} [{(sec x)}^{2}]$ $[2]" "=d/dx[(secx)^2]$

Use power rule. We also have to use chain rule.

$[3] = 2 {(sec x)}^{1} \cdot \frac{d}{d x} (sec x)$ $[3]" "=2(secx)^1*d/dx(secx)$

Derivative of $sec x$ $secx$ is $sec x tan x$ $secxtanx$ .

$[4] = 2 (sec x) \cdot (sec x tan x)$ $[4]" "=2(secx)*(secxtanx)$

$[5] = 2 {sec}^{2} x tan x$ $[5]" "=2sec^2xtanx$