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17 lis 2020 · To find the derivative of \(y = \text{arcsec}\, x\), we will first rewrite this equation in terms of its inverse form. That is, \[ \sec y = x \label{inverseEqSec}\] As before, let \(y\) be considered an acute angle in a right triangle with a secant ratio of \(\dfrac{x}{1}\).
The derivative of the inverse secant function is equal to 1/(|x|√(x 2-1)). We can prove this derivative using the Pythagorean theorem and algebra. In this article, we will learn how to derive the inverse secant function.
25 lip 2023 · Formula. The arcsec derivative can be expressed using calculus notation as d/dx (arcsec (x)). To find the derivative, we use the inverse trigonometric identity d/dx (arcsec (x)) = 1 / (|x|√ (x^2 – 1)). It is worth noting that this formula holds true for x ∈ (-∞, -1) and x ∈ (1, +∞).
Review the derivatives of the inverse trigonometric functions: arcsin(x), arccos(x), and arctan(x).
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The derivatives of inverse trigonometric functions can be computed by using implicit differentiation followed by substitution.
