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

Problem

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

Solution

1. Identify the function as an exponential function of the form eu where u is a function of x

2. Apply the chain rule, which states that d(eu)/d(x)=eu⋅d(u)/d(x)

3. Determine the derivative of the exponent u=5*x which is (d(5)*x)/d(x)=5

4. Multiply the original exponential function by the derivative of the exponent.

5. Simplify the resulting expression.

Final Answer

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

Want more problems? Check here!