Estimate the given quantity. (Round the answer to three decimal places.) f(x) = 3e^{x}; ...

Question:

Estimate the given quantity. (Round the answer to three decimal places.)

{eq}f(x) = 3e^{x}; {/eq} estimate {eq}f'(1) {/eq}.

Derivative of Exponential Function:

The derivative of the exponential function is given by the following formula:

{eq}\frac {d}{dx} e^x =e^x {/eq}

To find out the value of the derivative at any value of an independent variable, simply put the value of the independent variable into the derivative.

Answer and Explanation:

Given:

{eq}f(x) = 3e^{x} \\ {/eq}

On derivating the above function, we get:

{eq}f'(x) = 3 e^{x} \\ {/eq}

On putting the value of 'x' i.e. x= 1 in the above calculated derivative, we get:

{eq}f'(1) = 3 e^{1} \\ =3e \\ = 3(2.718) \\ =8.1548 \\ =8.155 \\ {/eq}

which is the answer.


Learn more about this topic:

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Calculating Derivatives of Exponential Equations

from Math 104: Calculus

Chapter 9 / Lesson 5
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