Problem

Find the derivative of the following functions. $…

03:43

Problem 43 Hard Difficulty

Find the derivative of the following functions.
$$y=\sec x+\csc x$$

Answer

sec x tan - csc x cot x

Related Courses

Calculus 1 / AB

Calculus Early Transcendentals

Chapter 3

Derivatives

Section 5

Derivatives of Trigonometric Functions

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Video Transcript

so the question assets to find the derivative of seeking of X plus Cosi can't of X And before we begin, we can rewrite this in terms of signing co sign So we'll have one over co sign of X plus one over sign of X. And now because we have fractions, we can use the quotient rule. So we'll have why prime equals the derivative of the numerator. So zero times the denominator so co signer X minus the numerator times the derivative of the denominator minus sign of eggs all over the denominator squared. And this simplifies our first term will cancel out. We can distribute this negative, so that becomes Plus, So this first term simplifies to sign of X over co sine squared of X and we're just gonna highlight that below. Remember, we still have to do the quotient rule for this second term Here, one over sign of X So summer similarly will take the derivatives of the new married er zero times the denominator sign of X minus the numerator. So one times the denominator who sign of X all divided by sine squared Thanks and likewise this first term will cancel and we're left with co sign of X over science weird of acts. And now we can bring these two terms back together. So why prime equals sign of X over co sine squared of X minus co sign of X over sine squared and X And now we're gonna play around the little with our trigonometry. So for this first term, we get sign of X over co sign of X times one over Coastline of Axe. What we did is we broke this co sign apart minus and we're gonna do the same thing with this second term. So co sign of X over sign of X times one over sign of X. So we broke this denominator Signed Square Divac's And this can also be river in as tangent of X And this term can be written as c can't of X and now this term can lever in as co tangent of X. And this final term can be written as kusi can't have X and that yes, Allah derivative

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