`f(x) = 4^x` Find the derivative of the function

Thursday, December 1, 2011

$\displaystyle{f{{\left({x}\right)}}}={{4}}^{{x}}$ Find the derivative of the function

To find the derivative, we will use the following formula:

$\displaystyle\frac{{d}}{{{\left.{d}{x}\right.}}}{\left({{a}}^{{x}}\right)}={{a}}^{{x}}\cdot{\ln{{\left({a}\right)}}}\cdot{\left.{d}{x}\right.}$

By comparison, $\displaystyle{{a}}^{{x}}={{4}}^{{x}}$ then $\displaystyle{a}={4}$ , $\displaystyle{x}={x}$ , and $\displaystyle\frac{{d}}{{{\left.{d}{x}\right.}}}{\left({x}\right)}={1}$

Applying the formula, we get:

$\displaystyle{f{'}}{\left({x}\right)}={{4}}^{{x}}\cdot{\ln{{\left({4}\right)}}}\cdot{1}$

$\displaystyle={{4}}^{{x}}{\ln{{\left({4}\right)}}}$

So, $\displaystyle{f{'}}{\left({x}\right)}={{4}}^{{x}}{\ln{{\left({4}\right)}}}$ is the final answer

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Thursday, December 1, 2011

$\displaystyle{f{{\left({x}\right)}}}={{4}}^{{x}}$ Find the derivative of the function

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Thomas Jefferson's election in 1800 is sometimes called the Revolution of 1800. Why could it be described in this way?

Thursday, December 1, 2011

Find the derivative of the function

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Post a Comment

Thomas Jefferson&#39;s election in 1800 is sometimes called the Revolution of 1800. Why could it be described in this way?

$\displaystyle{f{{\left({x}\right)}}}={{4}}^{{x}}$ Find the derivative of the function

Thomas Jefferson's election in 1800 is sometimes called the Revolution of 1800. Why could it be described in this way?