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 = (x^2 - 2x + 2)e^(x)

Accepted Answer

Welcome back, everyone. Find D Y divided by DX4 Y equals X2 minus 4 X + 4, all multiplied by the power of X. For this problem, let's recognize that we have a product of two functions, right? So to find the derivative of why we're going to apply the product rule. According to the product rule, we're taking the derivative of the first function X2 minus 4 X + 4. And multiplying it by the second function E to the power of X. Then we are adding the first function X2 minus 4 X + 4, multiplied by the derivative of the second function E to the power of X. Now let's find each derivative. For X2 minus 4 X + 4, we're going to apply the power rule. The derivative of X2 is 2 X. The derivative of X is 1 we're subtracting 4, and the derivative of 4 is 0. That's a constant. This is multiplied by E to the power of X, and then we are adding X2 minus 4 X + 4. Multiplied by the derivative of eats the power of x which is eats the power of x itself. Now notice that we have a common factor so we can factor it out and combine the X terms and constants. We're going to get 2 X minus 4. Plus X2 minus 4 X + 4, so we're factoring out each to the power of X. And now we can Cancel out -4 and 4. And we are basically left with. X squared. Minus For X + 2 X. So that's -2 X when we combine those like terms, multiplied by each the power of X. And we can now factor out further because we have a common factor of X, right? Meaning we get X multiplied by the power of X and imprec we are left with X minus 2. So that's our final derivative and thank you for watching.

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

Watch next

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