13-26 Implicit differentiation Carry out the following steps.

Question

b. Find the slope of the curve at the given point.

cos y = x; (0, π/2)

Accepted Answer

Hi everyone, let's take a look at this practice problem dealing with implicit differentiation. This problem says, given the equation sin of X is equal to Y2d, use implicit differentiation to find the slope of the tangent line at the point of pi divided by 2.1. We're given 4 possible choices as our answers. For choice A, we have 0. for choice B, we have 1 divided by 2. For choice C, we have minus 1 divided by 2, and for choice D, we have 2. Now, we need to find the slope of our tangent line at the point of pi divided by 2.1, and we'll need to use implicit differentiation to find our derivative of Y with respect to X. So we were given the equation, sine of X. is equal to Y2. And so we're gonna need to take the derivative with respect to X of both sides of this equation. And in doing so, on the left hand side, when we take the derivative with respect to X of sin of X, I will get cosine of X. And this is going to be equal to, when I take the derivative of Y2d with respect to X, I will get 2 Y multiplied by the derivative of Y with respect to X. So here we've basically applied our chain rule. And so we need to solve this equation for the derivative of Y with respect to X, so I'll just divide both sides by 2 Y. And so, that means that the derivative of Y, with respect to X, It's going to be equal to cosine of X, divided by the quantity of toy. So we need to evaluate the slope of the tangent line at the point of high divided by 2.1. That means I'm gonna need to calculate my derivative of Y with respect to X at that point. So, in doing so, that means that our slope M is going to be equal to the derivative of Y, with respect to X at that point, which is going to be equal to the cosine. Of pi divided by 2. Divided by the quantity of 2 multiplied by 1. And by the way in this expression, this is going to be equal to the cosine of pi divided by 2 is 0, that gets divided by 2. And this is going to be equal to 0, since 0 divided by 2 is 0. And so this is the answer that I'm actually looking for. And if I compare that to my answer choices, I see that the correct answer choice corresponds to answer choice A. 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.
b. Find the slope of the curve at the given point.
cos y = x; (0, π/2)

Key Concepts

Implicit Differentiation

Slope of a Curve

Evaluating Derivatives at a Point

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