Question

Differentiate the function. y = e^(x² - 5).

Answer 1

To differentiate the function y = e^(x² - 5), we use the chain rule. The derivative is e^(x² - 5) multiplied by 2x.

Step-by-step explanation:

To differentiate the function y = ex² - 5, we can use the chain rule. The chain rule states that the derivative of a composite function is the derivative of the outer function multiplied by the derivative of the inner function.

Let's break the function down into its composite parts:

• Outer function: y = ex
• Inner function: u = x² - 5

To differentiate the outer function, we can use the derivative of the exponential function: d/dx(ex) = ex.

To differentiate the inner function, we can use the power rule: d/dx(x² - 5) = 2x.

Now, we can apply the chain rule: d/dx(ex² - 5) = ex² - 5 * 2x.