Find the Derivative - d/dx 10e^x

Problem

d()/d(x)*10*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.

2. Apply the constant multiple rule by moving the constant 10 outside of the derivative operator.

d()/d(x)*10*ex=10d(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 simply ex

d(ex)/d(x)=ex

4. Multiply the constant 10 by the result of the derivative.

10⋅ex=10*ex

Final Answer

d()/d(x)*10*ex=10*ex

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