Find the Derivative - d/dx 9e^x

Problem

d()/d(x)*9*ex

Solution

1. Identify the constant multiple rule, which states that the derivative of a constant times a function is the constant times the derivative of that function.

(d(c)*ƒ(x))/d(x)=cd(ƒ(x))/d(x)

2. Apply the constant multiple rule to the expression by moving the constant 9 outside of the derivative.

9d(ex)/d(x)

3. Recall the derivative rule for the natural exponential function, which states that the derivative of ex with respect to x is ex

d(ex)/d(x)=ex

4. Multiply the constant 9 by the result of the derivative to find the final expression.

9⋅ex

Final Answer

(d(9)*ex)/d(x)=9*ex

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