Find the derivative of the following functions.
y = cos ...

Question

Find the derivative of the following functions.

y = cos x/sin x + 1

Accepted Answer

Welcome back, everyone. In this problem, we want to calculate the derivative of Y equals x x + 2 divided by X minus 7. A says the derivative is sec X multiplied by 20 X plus se X. B says it's KX multiplied by 2 X plus cos X. C negative X multiplied by +21 X plus X, and D, negative co X multiplied by 2 X plus cos X. Now, before we differentiate Y, it would be probably easier for us to separate the first fraction into two fractions. That will allow us to avoid the quotient rule and differentiate a bit more easily. Because no, given why. Is equal to sin x + 2 divided by cus X. Plus 7. OK. Then if we separate it, this is gonna be sin x divided by cost X. Plus 2 divided by class X. -7. No, if we apply our trigonometric identities here, OK, recall that sine divided by cosine equals the tangent. So really then Y, the first term here is going to be the tangent of X. Next, recall that the scant is the reciprocal of a cosine function. Therefore, we could rewrite this as 2 multiplied by X. So Y equals 10 X + 2X minus 7. No, we can go ahead and differentiate, OK? So now differentiating Y. Differentiating Y with respect to X, OK. Notice here we have 3 terms, so we'll need to differentiate each of them. Now what do we know about these these terms? Well, the derivative of the tangent is the square of the sand. So now, to differentiate an X, we can write down the square of a c X, OK. So C can squared X or 6 squared X and know we can multiply it by the derivative of the argument where the derivative of the tangent of the derivative of X is 1, OK, so that's 1 multiplied by 6 square X which would just give us 6 grade X. Next, the derivative of the scant is the scant multiplied by the tangent, OK? So we could rewrite this then as 2 multiplied by sec X 0 X, OK, multiplied again by the derivative of the arguments which is 1. And no, the derivative of negative 7 is 0 because negative 7 is a constant. Now that we've evaluated each derivative, we can simplify this. To be 6 squared X plus 2 6 X 0 X. And now notice that both terms have the Ccant in common. So if we factor out 6 X, then we are left with 2 times X. Plus X. Thus, the derivative of Y with respect to X isEX multiplied by 20 X plusse X. If we look back at our answer choices, that means A is the correct answer. Thanks a lot for watching everyone. I hope this video helped.

Find the derivative of the following functions.
y = cos x/sin x + 1

Key Concepts

Derivative

Trigonometric Functions

Quotient Rule

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