Common Calculus Mistakes
Derivative of an exponential function

The Goal

Find

goal


The Mistake

Find the mistake:

mistake

Need a hint? Look carefully at the red part:

mistake

The Correction

correction


An Explanation

An exponential function is not a power function, so the power rule can not be used to find its derivative. A power function has the independent variable (t in this context) in the base of the function, as in t3. An exponential function has the independent variable in the exponent of the function, as in et. Use the formula for the derivative of an exponential function in this case!

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