Problem

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

Problem 27 Easy Difficulty

Find the derivatives of the given functions.
$$y=\frac{1}{3} \tan ^{3} x-\tan x$$

Answer

$\frac{d y}{d x}=\sec ^{2} x\left(\tan ^{2} x-1\right)$

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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

we want to find the derivative Dy dx for the function Y equals one third tan cube X minus tangent of X. To find this directive, we're going to rely on the throat of shortcuts. We picked up to a single variable cup in particular, we're going to use an electric diverse events we've recently learned to solve. So these derivatives are the six derivatives that are here in particular. We're gonna need to use the tangent derivative which is you cant squared X. We're also going to make use of a chain rule in this problem. So we can write our function as Y equals one third. Can xq minus 10 X. This makes it easier to see how the chain rule is used in the first term. That's we proceeded the derivation. So the derivative dy dx is as follows. Dy dx equals one third times three times square accepts. You can't squared X. This is the tangent derivative in the chain rule. The first term minus. You can't squared X, simply the tangent derivative. Thus factoring out sequence can't squared X. We have violence solution. DY DX is equal to you can't squared X times 10 squared x minus one.

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Allyn J. Washington, Richard S. Evans

Basic Technical Mathematics with Calculus

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