Find the Derivative - d/dx y=e^(7x)

Problem

d(e(7*x))/d(x)

Solution

1. Identify the rule needed for the derivative of an exponential function with a composite exponent, which is the Chain Rule.

2. Apply the formula for the derivative of eu where u=7*x The derivative is eu⋅d(u)/d(x)

3. Differentiate the inner function u=7*x with respect to x which results in 7

4. Multiply the derivative of the outer function by the derivative of the inner function to get e(7*x)⋅7

5. Simplify the expression by placing the constant coefficient in front.

Final Answer

d(e(7*x))/d(x)=7*e(7*x)

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