Problem

Find the derivatives of the given functions. $$y=…

Problem 8 Easy Difficulty

Find the derivatives of the given functions.
$$y=\sec \sqrt{1-4 x}$$

Answer

$\frac{d u}{d x}=-\frac{2 \sec \sqrt{1-4 x} \tan \sqrt{1-4 x}}{\sqrt{1-4 x}}$

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Calculus 1 / AB

Basic Technical Mathematics with Calculus

Chapter 27

Differentiation of Transcendental Functions

Section 2

Derivatives of the Other Trigonometric Functions

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Video Transcript

All right. We want to take the derivative with respect to X. Do I. D. X. Or function? Why is equal to the C. Cat of the square root of one minus four X. To do so we're going to rely on derivative shortcuts. We picked up through a single variable cap in particular. We're going to be relying on trigonometry derivatives we recently learned. So the most relevant rules are here. The trick brothers are DDX mexicans, Cossacks, DDX Cossacks is negative sign etcetera. We also know the chain rule, products rule quotient rule and so on. In this particular problem we're gonna have to rely on the chain rule as well as a derivative C. Camp to solve. So we can rewrite why as C can't one minus four actually one half this makes using the chain little bit simpler. Thus we cannot solve. So do I. D. X. C can't route one minus four. X 10 1 minus four X. This is via the C. Can derivative multiplied by one half times one minus four X. Negative one half to the negative four. This is by the double chain rule on one minus four X. Or rather on square root one minus four X. The final solution to the bottom dy dx equals negative to see Can't route one minus four X 10, 1 minus four X. All over the square root of one minus four X.

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Allyn J. Washington, Richard S. Evans

Basic Technical Mathematics with Calculus

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