Find d y y=sec(x^2-1)

Name: Problem 28, Chapter 3: University Calculus: Early Transcendentals
Uploaded: 2020-05-03T17:08:48-08:00
Duration: 1 min 30 s
Channel: Linh Vu
Description: Find d y y=sec(x^2-1)

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Key Concepts

Chain Rule

The chain rule is a method for differentiating composite functions by taking the derivative of the outer function evaluated at the inner function and multiplying it by the derivative of the inner function. This rule is essential when you need to differentiate a function like sec(x² - 1), where the input to the secant function is itself a function of x.

Derivative of Secant Function

The derivative of the secant function is given by d/dx(sec(u)) = sec(u)tan(u)du/dx, where u is a function of x. This formula is crucial for finding the derivative of y = sec(x² - 1), as it directly applies once the overall structure of the function is acknowledged.

Polynomial Differentiation

Differentiating the polynomial inside the composite function involves using the power rule. In this case, for the inner function u = x² - 1, the derivative is computed as du/dx = 2x, which is a straightforward application of the power rule. This step is necessary when applying the chain rule.

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