Evaluate and simplify y'.
x = cos (x−y)

Question

Evaluate and simplify y'.

x = cos (x−y)

Accepted Answer

Welcome back, everyone. Evaluate and simplify Z given T equals sign off T + Z. We're given the foreign answer choices A says Z equals cosine of T + Z minus 1. B says sant of T + C + 1. C says equant of T + Z minus 1 and D says that Z is equal to cosine of T + Z + 1. So essentially we want to understand that C is a function of T such that C equals Z of T. And we're going to apply implicit differentiation to solve for Z. So on the left, we're given C, we have to take T derivative, and on the right, we have to differentiate sine of T plus C because the equation holds, we can differentiate both sides and the equation will still hold. So the derivative of T is essentially DT divided by DT, which is 1, or we can just use the power rule. And for the right hand side we want to evaluate the derivative of sine of T + C. Let's recall that the derivative of sine of X is cosine of X. So in this case we're going to get cosine of T + C, but we have an inner function which means that we also need to multiply by the derivative of T + C based on the chain rule. So we get 1 equals cosine of T + C multiplied by the derivative of T, which is 1, we already know that, and then plus the derivative of Z. And the derivative of C is exactly what we're looking for, so we want to distribute the terms which gives us 1 equals cosine of T + C plus Z cosine of T + C. Now let's isolate the final term. Which means that we have to subtract 1 minus cosine of T + C and set it equal to C cosine of T + C. And now solving for C, we have to divide both sides by cosine of T + C, so we get 1 minus cosine of T + C. Divided by cosine of T + C. Let's divide. So first of all, we have one divided by cosine of T + C. By definition, this is 2 of T + C. And then we have minus cosine of T + Z divided by cosine of T + Z. So this gives us -1. So that's our final answer. Z 2 of T + Z minus 1, which essentially corresponds to the answer choice C. Thank you for watching.

Evaluate and simplify y'.
x = cos (x−y)

Key Concepts

Implicit Differentiation

Chain Rule

Solving for y'

Watch next

Evaluate and simplify y'.x = cos (x−y)

Key Concepts

Implicit Differentiation

Chain Rule

Solving for y'

Watch next

Evaluate and simplify y'.
x = cos (x−y)