In Exercises 7–26, find the derivative of y with respect to x,...

Question

In Exercises 7–26, find the derivative of y with respect to x, t, or θ, as appropriate.

y = e^(5-7x)

Accepted Answer

Welcome back, everyone. Differentiate Y equals E to the power of 2 minus 5 X with respect to X. A 5 E to the power of 2 minus 5 X B 5 E to the power of 2 minus 5 X. C E to the power of 2 minus 5 X, and D-2 E to the power of 5. For this problem, let's recognize that Y is a composite function. We can set our exponent equal to U. A U equals 2 minus 5 X so that we can express Y as E to the power of U. And now clearly we are going to differentiate Y with respect to X using the chain rule. First of all, we're going to differentiate Y with respect to U and multiply by the derivative of U with respect to X. So let's identify the derivative DY divided by DU. Which is the derivative of eats the power of you and thus eats the power of you. We can immediately express it in terms of X, that's E to the power of 2 minus 5 X. And now the derivative of u with respect to X is the derivative of 2 minus 5 X, which is equal to 0, where differentiating a constant minus 5 multiplied by the derivative of X, which is 1. So we simply get -5. Now, multiplying these, we get -5, multiplied by E to the power of 2 minus 5 X. Considering the answer choices, we can conclude that the correct answer is option A. Thank you for watching.

In Exercises 7–26, find the derivative of y with respect to x, t, or θ, as appropriate.y = e^(5-7x)

Watch next

In Exercises 7–26, find the derivative of y with respect to x, t, or θ, as appropriate.
y = e^(5-7x)