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 = cos(e^(-θ^2))

Accepted Answer

Welcome back, everyone. Find D Y divided by DX for Y equals sign of each to the power of 3 x 2. For this problem we want to find the derivative of a composite function. Let's remember that whenever we have a composite function, we have to apply the chain rule. So, the outer function is sign, which essentially means that first of all, we're differentiating sign. Of e to the power of 3 x2 with respect to the first inner function. And that's e to the power of 3 x 2. According to the chain rule, we're multiplying by the derivative of the first inner function that's e to the power of 3 X2. With respect to the next inner function, and that's 3 X2, the exponent, right? So D of 3 X2. And finally, we have our final. In our function, so we're multiplying by the derivative of 3 x 2d with respect to x. Now we want to compute three derivatives, starting with sine. Let's remember that the derivative of sine is cosine. So we get cosine of the angle E to the power of 3 x 2. For the second derivative, let's remember that the derivative of eats the power of Xs eats the power of X. So in this case, because X is replaced with 3 x 2 we're multiplying by the power of 3 X2, and then the derivative of 3 X2d is going to be found using the power rule. We multiplied by. The derivative of X squared is 2 X. Now let's simplify. We're going to get 6 eggs. Followed by its the power of 3 x 2, followed by cosine of its the power of 3 x 2. Which is our final answer for this problem? Thank you for watching.

In Exercises 7–26, find the derivative of y with respect to x, t, or θ, as appropriate.y = cos(e^(-θ^2))

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In Exercises 7–26, find the derivative of y with respect to x, t, or θ, as appropriate.
y = cos(e^(-θ^2))