`h(x) = 1/4sinh(2x) - x/2` Find the derivative of the function

Sunday, September 5, 2010

$\displaystyle{h}{\left({x}\right)}=\frac{{1}}{{4}}{\sinh{{\left({2}{x}\right)}}}-\frac{{x}}{{2}}$ Find the derivative of the function

$\displaystyle{h}{\left({x}\right)}=\frac{{1}}{{4}}{\sinh{{\left({2}{x}\right)}}}-\frac{{x}}{{2}}$

To take the derivative of this function, refer to the following formulas:

$\displaystyle\frac{{d}}{{\left.{d}{x}}}{\left({u}\pm{v}\right)}=\frac{{{d}{u}}}{{\left.{d}{x}}}\pm\frac{{{d}{v}}}{{\left.{d}{x}}}$

$\displaystyle\frac{{d}}{{{\left.{d}{x}\right.}}}{\left[{\sinh{{\left({u}\right)}}}\right]}={\cosh{{\left({u}\right)}}}\cdot\frac{{{d}{u}}}{{\left.{d}{x}}}$

$\displaystyle\frac{{d}}{{\left.{d}{x}}}{\left({c}{u}\right)}={c}\cdot\frac{{{d}{u}}}{{\left.{d}{x}}}$

$\displaystyle\frac{{d}}{{\left.{d}{x}}}{\left({c}{x}\right)}={c}$

Applying them, h'(x) will be

$\displaystyle{h}'{\left({x}\right)}=\frac{{d}}{{\left.{d}{x}}}{\left[\frac{{1}}{{4}}{\sinh{{\left({2}{x}\right)}}}-\frac{{x}}{{2}}\right]}$

$\displaystyle{h}'{\left({x}\right)}=\frac{{d}}{{\left.{d}{x}}}{\left[\frac{{1}}{{4}}{\sinh{{\left({2}{x}\right)}}}\right]}-\frac{{d}}{{\left.{d}{x}}}{\left(\frac{{x}}{{2}}\right)}$

$\displaystyle{h}'{\left({x}\right)}=\frac{{1}}{{4}}\frac{{d}}{{\left.{d}{x}}}{\left[{\sinh{{\left({2}{x}\right)}}}\right]}-\frac{{d}}{{\left.{d}{x}}}{\left(\frac{{x}}{{2}}\right)}$

$\displaystyle{h}'{\left({x}\right)}=\frac{{1}}{{4}}\cdot{\cosh{{\left({2}{x}\right)}}}\cdot\frac{{d}}{{\left.{d}{x}}}{\left({2}{x}\right)}-\frac{{1}}{{2}}$

$\displaystyle{h}'{\left({x}\right)}=\frac{{1}}{{4}}\cdot{\cosh{{\left({2}{x}\right)}}}\cdot{2}-\frac{{1}}{{2}}$

$\displaystyle{h}'{\left({x}\right)}=\frac{{1}}{{2}}{\cosh{{\left({2}{x}\right)}}}-\frac{{1}}{{2}}$

Therefore, the derivative of the function is $\displaystyle{h}'{\left({x}\right)}=\frac{{1}}{{2}}{\cosh{{\left({2}{x}\right)}}}-\frac{{1}}{{2}}$ .

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Sunday, September 5, 2010

$\displaystyle{h}{\left({x}\right)}=\frac{{1}}{{4}}{\sinh{{\left({2}{x}\right)}}}-\frac{{x}}{{2}}$ 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?

Sunday, September 5, 2010

Find the derivative of the function

No comments:

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?

$\displaystyle{h}{\left({x}\right)}=\frac{{1}}{{4}}{\sinh{{\left({2}{x}\right)}}}-\frac{{x}}{{2}}$ 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?