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).
Determine the first derivative of e^x^3
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