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Derivatives of Exponential Functions TS: Explicitly Assessing Information and Drawing Conclusions. Objective. To find the derivatives of natural exponential functions. Derivatives of Exponential Functions. What is the derivative?. Super Guess:. Derivatives of Exponential Functions.
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Derivatives of Exponential FunctionsTS: Explicitly Assessing Information and Drawing Conclusions
Objective • To find the derivatives of natural exponential functions.
Derivatives of Exponential Functions What is the derivative? Super Guess:
Derivatives of Exponential Functions What is the derivative? Super Guess: WRONG This is incorrect. This rule works for f (x) = xN, when the base is a variable x and the exponent is a constant N. The power rule does not apply to exponential functions.
Derivatives of Exponential Functions What is the derivative? CORRECT!
Derivatives of Exponential Functions • Use the chain rule to find the derivative of the composition of the natural exponential function and another function.
Derivatives of Exponential Functions • The derivative of an exponential function of the formf (x) = euis the product of the function and the derivative of its exponent.
Derivatives of Exponential Functions • Differentiate: Derivative of 5x is 5 Derivative of eu is eu
Derivatives of Exponential Functions • Differentiate: Derivative of x3 is 3x2 Derivative of eu is eu
Derivatives of Exponential Functions • Differentiate: Derivative of 3x2 is 6x Derivative of eu is eu
Derivatives of Exponential Functions • Differentiate: Derivative of x-3 is -3x-4 Derivative of eu is eu
Derivatives of Exponential Functions • Differentiate: Product Rule
Derivatives of Exponential Functions • Differentiate: Quotient Rule
Derivatives of Exponential Functions • Differentiate:
Derivatives of Exponential Functions • Differentiate:
Derivatives of Exponential Functions • Differentiate: Product Rule
Derivatives of Exponential Functions • Differentiate: Quotient Rule
Conclusion • The derivative of the natural exponential function is itself. • The derivative of an exponential function of the formf (x) = euis the product of the function and the derivative of its exponent.