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Solve the given problems.On a calculator, find the values of (a) $\sec ^{2} 1.0000$ and(b) $(\tan 1.0001-\tan 1.0000) / 0.0001 .$ Compare the values and give the meaning of each in relation to the derivative of tan $x$ where $x=1$

Calculus 1 / AB

Chapter 27

Differentiation of Transcendental Functions

Section 2

Derivatives of the Other Trigonometric Functions

Derivatives

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First problem, we want to solve the given problem using a calculator. So this is going to be 37. We see, or 39. We have the values of second squared of one. And then we want to look at tangent Of 1.001 Minour Tangent of one, all divided by 0.001. We end up being a very close value to seeking square. And the reason why is because this is uh, for example, what happens when we take a small change and why over a small change in X a small change and why over a small change in X is known as the derivative. So we see that the derivative of the tangent at one is equal to seek and square one.

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