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^(θ)(sinθ + cosθ)

Accepted Answer

Welcome back, everyone. Differentiate with respect to S. Y equals eats the power of S multiplied by cosine of S plus sine of S. A eats the power of S multiplied by cosine S minus sine S. B eats the power of S multiplied by cosine S plus sine S. C. 2 eats the power of S sins, and D2 eats the power of S cosines. For this problem, let's recognize that Y is a product of two functions, so we're going to apply the product rule for differentiation. Y is going to be the derivative of the first function, so that's the derivative of it's the power of S, multiplied by the second function, which is cosine of S plus sine of S. Plus, the first function, which is to the power of S multiplied by the derivative of the second function. So the derivative of cosine of S plus sine of s. And now let's find each derivative. The derivative of E to the power of S is E to the power of S. And we get each the power of S multiplied by cosine of S plus sine of S. And we are adding it to the power of S. Which is multiplied by the derivative of cosine of S plus sine of S. Now, the derivative of cosine is negative sign, so we get negative sign of S, and the derivative of sine is cosine, so we're adding cosine of S. Now we can factor out it's the power of S and imprecs we have. Cosine offs. Plus sign of S minus sign of S. Plus cosine of S. Notice that we can cancel out the sign. And we have two cosines, so that would be 2 E to the power of S cosine S. Which corresponds to the answer choice D. Thank you for watching.

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

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