Determine the first derivative of e^x^3

Answer 1

To find the first derivative of e^(x^3), we can use the chain rule.

Let's denote y = e^(x^3).

Using the chain rule, the first derivative is given by:

dy/dx = d(e^(x^3))/dx

To apply the chain rule, we need to differentiate the outer function e^(x^3) with respect to its "inner" function, which is x^3.

The derivative of e^(x^3) with respect to x^3 can be obtained by simply multiplying e^(x^3) by the derivative of x^3 with respect to x, which is 3x^2.

Therefore, dy/dx = (e^(x^3)) * (3x^2)

Therefore, the first derivative of e^(x^3) is 3x^2 * e^(x^3).