13-26 Implicit differentiation Carry out the following steps.

Question

a. Use implicit differentiation to find dy/dx.

cos y = x; (0, π/2)

Accepted Answer

Hi everyone, let's take a look at this practice problem. This problem says, given the equation sin of x is equal to Y2, use implicit differentiation to find the derivative of Y with respect to X. We're given 4 possible choices as our answers. For choice A, we have the sin of x divided by the quantity of 2 Y. For choice B, we have minus sign of x divided by the quantity of 2 Y. For choice C, we have cosine of x divided by the quantity of 2 Y. And for choice D, we have minus cosine of x divided by the quantity of 2 Y. Now, we're asked to find the derivative of Y with respect to X by using implicit differentiation. So I'm gonna take our equation that we're given, which is sin of X. is equal to Y2, and I'm going to take a derivative with respect to X of both sides of this equation. So doing so on the left hand side, when I take a derivative of sin of X with respect to X, I will get cosine of X. And this is going to be equal to on the right hand side, I have to apply our power rule and chain rule to take the derivative of Y2 with respect to X. And so when I apply both of those rules, I'll get 2 multiplied by Y multiplied by the derivative of Y with respect to X. So I need to solve this equation for the derivative of Y with respect to X by dividing both sides by the quantity of 2 Y. In doing so, I will get the derivative of Y with respect to X is equal to cosine of X. Divided by the quantity of 2 y. So this is the answer that we're actually looking for. And if we compare our answers to our answer choices, we see that the correct answer choice corresponds to answer choice C. So, I hope that this explanation has been useful, and I'll see you in the next video.

13-26 Implicit differentiation Carry out the following steps.a. Use implicit differentiation to find dy/dx.cos y = x; (0, π/2)

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13-26 Implicit differentiation Carry out the following steps.
a. Use implicit differentiation to find dy/dx.
cos y = x; (0, π/2)