Find the Derivative - d/dx y=4ex^2

Problem

d()/d(x)*4*e(x2)

Solution

1. Identify the constant multiple rule, which allows the constant 4 to be moved outside the derivative.

(d(4)*e(x2))/d(x)=4d(e(x2))/d(x)

2. Apply the chain rule for the exponential function, where the derivative of eu is eu⋅d(u)/d(x)

d(e(x2))/d(x)=e(x2)⋅d(x2)/d(x)

3. Differentiate the inner function x2 using the power rule.

d(x2)/d(x)=2*x

4. Multiply the results together to find the final derivative.

4⋅e(x2)⋅2*x=8*x*e(x2)

Final Answer

(d(4)*e(x2))/d(x)=8*x*e(x2)

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