In Exercises 59–86, find the derivative of y with respect to t...

Question

In Exercises 59–86, find the derivative of y with respect to the given independent variable.

71. y = log₂(5θ)

Accepted Answer

Welcome back, everyone. Compute DY divided by DC4. Y equals log of base 3 of 2 T. A says 1 divided by TLN of 3, B 2 divided by TLN of 3, C 1 divided by 2 TLN of 3, and D 1 divided by T. For this problem, let's recognize that Y is a composite function, and we can set our inner function equal to U. So in this case, our inner function is 2 T and U becomes 2 T. So Y is equal to log of base 3 of U. So to differentiate why. In other words, to compute DY divided by DT we're going to use the chain rule. First we have to differentiatey with respect to u and multiply by the derivative of u with respect to C. Let's find each derivative, starting with Y with respect to you. This derivative is going to be the derivative of log of base 3 of you. Let's remember the rule. We're going to take 1 divided by our variable which is U, multiplied by LN of the base, which is LN of 3. And since we know what U is, we can substitute. This is going to be 1 divided by 2 TLN of 3. So we can already complete half of the equation, that's 1 divided by 2 TL and of 3. And we're going to multiply by the derivative of U with respect to T. That's the derivative of 2 T. we can factor out 2 and take the derivative of T, which is 1. So 2 multiplied by 1 gives us 2. Finally, we can cross out the two, and we can show that the final answer is 1 divided by TLN of 3, which corresponds to the answer choice A. Thank you for watching.

In Exercises 59–86, find the derivative of y with respect to the given independent variable.71. y = log₂(5θ)

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In Exercises 59–86, find the derivative of y with respect to the given independent variable.
71. y = log₂(5θ)