Sunday, November 27, 2022

$sec^{-1} x^2$ Derivative | What is derivative of sec x^2?

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Hello everyone. You can reach derivative of $sec^{-1} x^2$ in this lesson. We wish you good work.

sec -1 derivative

What is derivative of $sec^{-1} x^2$?

$Sec^{-1} u$ derivative formulas:

$\frac{d}{dx}sec^{-1} u=\frac{1}{|u|.\sqrt{u^2-1}}.\frac{du}{dx}$

Now let's answer our question.

Differentiate $y=sec^{-1} x^2$

Solution For $x^2$ > 1 > 0,

>>> $\frac{dy}{dx}=\frac{1}{|x|\sqrt{(x^2)^2-1}}.\frac{d}{dx}x^2$

>>> $=\frac{2x}{x^2\sqrt{x^4-1}}=\frac{2}{x.\sqrt{x^4-1}}$

Answer = $\frac{2}{x.\sqrt{x^4-1}}$