Find the Derivative - d/dx 5e^(5x)

Problem

d()/d(x)*5*e(5*x)

Solution

1. Identify the constant multiple rule, which allows the constant 5 to be moved outside the derivative.

d()/d(x)*5*e(5*x)=5d(e(5*x))/d(x)

2. Apply the chain rule for the exponential function eu where u=5*x

d(eu)/d(x)=eud(u)/d(x)

3. Differentiate the exponent 5*x with respect to x

(d(5)*x)/d(x)=5

4. Multiply the results together to find the derivative of the composite function.

5d(e(5*x))/d(x)=5*(e(5*x)⋅5)

5. Simplify the expression by multiplying the constants.

5⋅5*e(5*x)=25*e(5*x)

Final Answer

(d(5)*e(5*x))/d(x)=25*e(5*x)

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