What is d/dx e^2?

which means calculate

Question

What is d/dx e^2?

which means calculate

BlackTom AI · Accepted Answer

The expression is d/dx e^2, meaning we differentiate e raised to the constant power 2 with respect to x. Since 2 is a constant, e^2 is simply a constant value, not a function of x. With respect to x, the derivative of any constant is zero.

Option 1: 2. This would be the derivative if the exponent were variable and equal to x, for example d/dx e^x = e^x. Here the exponent is the constant 2, not x, so this is incorrect.

Option 2: 2 e^2. This would suggest that the derivative yields a multiple of the original constant, as if the exponent depended on x in a linear fashion, which it does not. The derivative of a constant is zero, not a scaled constant.

Option 3: 0. This matches the fact that e^2 is a constant and its derivative with respect to x is zero. Conceptually, constant functions have zero slope.

Option 4: 2 e. This implies a linear function in x with slope 2, or a derivative that scales by e, neither of which applies when differentiating a constant like e^2 with respect to x.

ERMCPS5350_003_2025_3 - INTRO TO QUANTITATIVE RISK MANAGEMENT 10. Quiz for Class 10

What is d/dx e^2? which means calculate

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