If y=ex4𝑦=𝑒𝑥4, find dydx.

To find the derivative of the function y = e^(x^4), we will use the chain rule. The chain rule states that the derivative of a composite function is the derivative of the outer function times the derivative of the inner function.

Step 1: Identify the outer and inner functions. Here, the outer function is e^u and the inner function is x^4.

Step 2: Find the derivative of the outer function. The derivative of e^u with respect to u is e^u.

Step 3: Find the derivative of the inner function. The derivative of x^4 with respect to x is 4x^3.

Step 4: Apply the chain rule. The derivative of y with respect to x is the derivative of the outer function times the derivative of the inner function.

So, dy/dx = e^(x^4) * 4x^3.